example-1Multiple choice
A prism is a polyhedron whose lateral faces are
- (a)Circles
- (b)Triangles
- (c)Parallelograms
- (d)Rhombuses or Rhombi
Show solution
Solution : Correct answer is (c).
Chapter 6
Class 8 Mathematics · 101 questions · 85 with answers
Solved examples
example-2Multiple choice
A pyramid is a polyhedron whose lateral faces are
- (a)Rectangles
- (b)Triangles
- (c)Parallelograms
- (d)Rhombuses or Rhombi
Show solution
Solution : Correct answer is (b). In examples 3 and 4, fill in the blanks to make the statements true
example-3Fill in the blanks
In a regular polyhedron ______ number of faces meet at each vertex.
Show solution
Solution : same.
example-4Fill in the blanks
A pentagonal prism has ______ edges.
Show solution
Solution : 15. In examples 5 and 6, state whether the statements are true or false.
example-5Short answer
A sphere is a polyhedron.
Show solution
Solution : False.
example-6Short answer
In a prism the lateral faces need not be congruent
Show solution
Solution : True.
example-7Short answer
Draw the top, front and side views of the given solid.
Show solution
Solution : Front view Top view Side view Use a compass and straight edge to create a larger version of each net on a cardboard. Fold each net into a polyhedron. REGULAR POLYHEDRONS NAME FACES EXAMPLE NET Tetrahedron 4 triangles Octahedron 8 triangles Icosahedron 20 triangles Cube 6 squares Dodecahedron 12 pentagons
example-8Short answer
Use isometric dot paper to sketch a rectangular prism with length 4 units, height 2 units and width 3 units.
Show solution
Solution : Steps: (1) Draw a parallelogram with sides 4 units and Width 3 units. Length This is top of the prism Fig.1 (Fig 1). (2) Start at one vertex. Draw a line passing Height through two dots. Repeat for other three vertices. Draw the Fig. 2 hidden edges as dashed line (Fig 2). (3) Connect the ends of the lines to complete the prism (Fig 3). Fig. 3 1. Complete the table for POLYHEDRON V E F V-E+F the number of vertices V, edges E and faces F Tetrahedron for each of the polyhedrons you made. Octahedron 2. Make a Conjecture What do you think is Icosahedron true about the relationship between Cube the number of vertices, Dodecahedron edges and faces of a polyhedron?
example-9Short answer
Identify the shape whose net is given below.
Show solution
Solution : This shape is entirely made of equilateral triangles. When folded, it results in a regular octahedron. Note that since these are all equilateral and congruent faces, it is a regular polyhedron. A polyhedron is formed by four or more polygons that intersect only at their edges. The faces of a regular polyhedron are all congruent regular polygons and the same number of faces intersect at each vertex, Regular polyhedrons are also called Platonic solid. There are exactly five regular polyhedrons.
example-10Short answer
The solid given below is a rectangular prism or cuboid. Make all the diagonals of this shape.
Show solution
Solution : There are only four diagonals as shown below. Note that in a 3D shape, diagonals connect two vertices that do not lie on the same face. E.g. the line segment from A to H in figure below is not a diagonal for the solid. Diagonals must pass through the inside of the shape. However, AH is diagonal of face ADHE.
example-11Short answer
Count the number of cubes in the given shapes.
Show solution
Solution : (i) 8 cubes (ii) 6 cubes
example-12Multiple choice
Name the following polyhedrons and verify the Euler’s formula for each of them.
- (a)
- (b)
- (c)
Show solution
Solution : S. No Polyhedron F V F+V E F + V –E (a) Tetrahedron 4 4 8 6 2 (b) Cube 6 8 14 12 2 (c) Pentagonal 7 10 17 15 2 prism Volume, the space inside a three-dimensional object, is measured in cubic unit. If the blocks you build are each 1 cubic unit, then the volume of a block structure is equal to the number of blocks in the structure. For example, a structure made from eight blocks has a volume of 8 cubic units. If the blocks have an edge length of 1 cm, the structure’s volume is 8 cm3.
example-13Short answer
A polyhedron has 7 faces and 10 vertices. How many edges does the polyhedron have?
Show solution
Solution : For any polyhedron, F+V–E=2 Here, F = 7, V = 10, E = ? Using above formula, ⇒7 + 10 – E = 2 ⇒17 – E = 2 ⇒17 – 2 = E ⇒ Ε = 15
example-14Short answer
Find the number of vertices in a polyhedron which has 30 edges and 12 faces.
Show solution
Solution : For any polyhedron, F+V–E=2 Here, F = 12, V = ?, E = 30 Using above formula, 12 + V – 30 = 2 V – 18 = 2 V = 2 + 18 V = 20
example-15Short answer
The distance between City A and City B on a map is given as 6 cm. If the scale represents 1 cm = 200 km, then find the actual distance between City A and City B.
Show solution
Solution : Actual distance represented by 1cm = 200 km What is the surface area of a single block in square units? If the edge lengths of a block are 2 cm, what is the block’s surface area? What is the volume of the structure at the right in cubic units? What is the surface area of the structure above in square units? (Remember: Count only the squares on the outside of the structure.) Actual distance represented by 6 cm = 6 × 200 km = 1200 km So, actual distance between City A and City B is 1200 km.
example-16Short answer
Height of a building is 9 m and this building is represented by 9 cm on a map. What is the scale used for the map? Size drawn
Show solution
Solution : Scale of map = Actual size 9 cm 900 cm (because 9 m = 900 cm) Thus, scale is 1:100.
example-17Short answer
The scale on a map is 1 mm : 4 m. Find the distance on the map for an actual distance of 52 m.
Show solution
Solution : Distance on map for an actual distance of 4 m = 1 mm Distance on map for actual distance of 52 m 52 = 13 mm Thus, distance on map for actual distance of 52 m is 13 mm. All prisms have two identical, parallel faces. These two faces are always polygons. A prism’s other faces are always parallelograms. A prism is sometimes referred to by the shape of the two identical faces on its ends. For example, a triangular prism has triangular faces on its ends, and a rectangular prism has rectangular faces on its ends. Triangular Prism Rectangular Prism
example-18Short answer
Application of problem solving strategy Determine the number of edges, vertices and in the following figure:
Show solution
Solution : Understand and Explore the problem • What information is given in the question? A cube with one of its corner cut. • What are you trying to find? The no. of edges, vertices and faces. • Is there any information that is not needed? The measures of edges are not needed. Plan a strategy • Think of the definitions of an edge, vertex and faces and try to co-relate them to the figure given above. Solve • The polygonal regions are called faces, hence there are 7 faces. • The line segment formed by the intersection of two faces is called edges, hence there are 15 edges. • Edges meet at vertices which are points, hence there are 10 vertices. Revise • The above answer is verified using Euler’s Formula. F+V=E+2 For the above problem, F = 7, V = 10, E = 15 F + V = 7 + 10 = 17 E + 2 = 15 + 2 = 17 Hence F + V = E + 2 is verified. These figures are prisms. These figures are not prisms. In each of the questions 1 to 21, out of four options only one is correct. Write the correct answer. 1. Which amongst the following is not a polyhedron? (a) (b) (c) (d) 2. Which of the following will not form a polyhedron? (a) 3 triangles (b) 2 triangles and 3 parallelogram (c) 8 triangles (d) 1 pentagon and 5 triangles 3. Which of the following is a regular polyhedron? (a) Cuboid (b) Triangular prism (c) Cube (d) Square prism
Questions
Q1Short answer
2. Front Top Side Front Top Side
Show answer
(c)
Q3Long answer
The views below represent a three-dimensional figure that cannot be built from cubes. Determine which three-dimensional figures match the views. A B C D Front Top Side • Scale is the relationship between the drawing’s/model’s dimensions to the actual object’s dimensions. • In a map, symbols are used to depict the different objects and places. • Maps involve a scale which is fixed for a particular map. Explain how you would find the surface area of an open-top box that is shaped like a rectangular prism. Describe the shapes in a net used to cover a cylinder. In examples 1 and 2, write the correct answer from the given four options.
Show answer
(c)
Q4Multiple choice
Which of the following is a two Dimensional figure?
- (a)Rectangle
- (b)Rectangular Prism
- (c)Square Pyramid
- (d)Square Prism
Show answer
(a) Rectangle
Q5Multiple choice
Which of the following can be the base of a pyramid?
- (a)Line segment
- (b)Circle
- (c)Octagon
- (d)Oval
Show answer
(c) Octagon
Q6Multiple choice
Which of the following 3D shapes does not have a vertex?
- (a)Pyramid
- (b)Prism
- (c)Cone
- (d)Sphere
Show answer
(d) Sphere
Q7Multiple choice
Solid having only line segments as its edges is a
- (a)Polyhedron
- (b)Cone
- (c)Cylinder
- (d)Polygon What do all the prisms have in common? How are the non-prisms different from the prisms?
Show answer
(a) Polyhedron
Q8Multiple choice
In a solid if F = V = 5, then the number of edges in this shape is
- (a)6
- (b)4
- (c)8
- (d)2
Show answer
(c) 8
Q9Multiple choice
Which of the following is the top view of the given shape?
- (a)
- (b)
- (c)
- (d)
Show answer
(a)
Q10Multiple choice
The net shown below can be folded into the shape of a cube. The face marked with the letter L is opposite to the face marked with which letter?
- (a)M
- (b)N
- (c)Q
- (d)O A net is a flat figure that can be folded to form a closed, three-dimensional object. Such an object is called a solid.
Show answer
(a) M
Q11Multiple choice
Which of the nets given below will generate a cone?
- (a)
- (b)
- (c)
- (d)
Show answer
(a)
Q12Multiple choice
Which of the following is not a prism?
- (a)
- (b)
- (c)
- (d)
Show answer
(b)
Q13Multiple choice
We have 4 congruent equilateral triangles. What do we need more to make a pyramid?
- (a)An equilateral triangle.
- (b)A square with same side length as of triangle.
- (c)2 equilateral triangles with side length same as triangle.
- (d)2 squares with side length same as triangle. 1. Explain how to find the surface area of a solid from the net for that solid. 2. Here is a net for a rectangular solid. Take whatever measurements you think are necessary to find the solid’s volume and surface area. Explain what measurements you took and what you did with them. The surface area of a three-dimensional object is the space covering the object’s surface. If you could pick up the object and flatten it so you could see all sides at once, the area of the flat figure would be the surface area. (Don’t forget to count the bottom surface!) Surface area is also measured in square units.
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(b) A square with same side length as of triangle.
Q14Multiple choice
Side of a square garden is 30 m. If the scale used to draw its picture is 1cm: 5m, the perimeter of the square in the picture is
- (a)20 cm
- (b)24 cm
- (c)28 cm
- (d)30 cm
Show answer
(b) 24 cm
Q15Multiple choice
Which of the following shapes has a vertex.
- (a)
- (b)
- (c)
- (d)
Show answer
(c)
Q16Multiple choice
In the given map, the distance between the places is shown using the scale 1 cm : 0.5 km. Then the actual distance (in km) between school and the book shop is General 4 cm Police store Station 2 cm School 2 cm 2.2 cm Book 5 cm Post shop Office
- (a)1.25
- (b)2.5
- (c)2
- (d)1.1 To become familiar with some of the vocabulary terms in the chapter, consider the following. 1. What does the term area total tell you about the meaning of surface area? 2. The word edge comes from the Latin word acer, meaning sharp. How does the Latin root help you define an edge of a three-dimensional figure? 3. The word vertex can mean peak or highest point. What part of a cone or pyramid is the vertex? 4. The word prism comes from the Greek word priein, meaning to saw. How might you describe a prism in terms of something sawn or cut off?
Show answer
(d) 1.1 To become familiar with some of the vocabulary terms in the chapter, consider the following. 1. What does the term area total tell you about the meaning of surface area? 2. The word edge comes from the Latin word acer, meaning sharp. How does the Latin root help you define an edge of a three-dimensional figure? 3. The word vertex can mean peak or highest point. What part of a cone or pyramid is the vertex? 4. The word prism comes from the Greek word priein, meaning to saw. How might you describe a prism in terms of something sawn or cut off?
Q17Multiple choice
Which of the following cannot be true for a polyhedron?
- (a)V = 4, F = 4, E = 6
- (b)V = 6, F = 8, E = 12
- (c)V = 20, F = 12, E = 30
- (d)V = 4, F = 6, E = 6
Show answer
(d) V = 4, F = 6, E = 6
Q18Multiple choice
In a blueprint of a room, an architect has shown the height of the room as 33 cm. If the actual height of the room is 330 cm, then the scale used by her is
- (a)1:11
- (b)1:10
- (c)1:100
- (d)1:3
Show answer
(b) 1:10
Q19Multiple choice
The following is the map of a town. Based on it answer question 19-21. The number of hospitals in the town is
- (a)1
- (b)2
- (c)3
- (d)4 There are two rectangular bases. There are four rectangular faces. The figure is a rectangular prism. There is one rectangular base. There are four triangular faces. The figure is a rectangular pyramid. There are two triangular bases. There are three rectangular faces. The figure is a triangular prism. There is one hexagonal base. There are six triangular faces. The figure is a hexagonal pyramid.
Show answer
(b) 2
Q20Multiple choice
The ratio of the number of general stores and that of the ground is
- (a)1 : 2
- (b)2 : 1
- (c)2 : 3
- (d)3 : 2
Show answer
(d) 3 : 2
Q21Multiple choice
According to the map, the number of schools in the town is
- (a)4
- (b)3
- (c)5
- (d)2 In questions 22 to 41, fill in the blanks to make the statements true.
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(c) 5
Q22Fill in the blanks
Square prism is also called a _______.
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cube
Q23Fill in the blanks
Rectangular prism is also called a ________.
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cuboid
Q24Fill in the blanks
In the figure, the number of faces meeting at B is ________.
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4
Q25Fill in the blanks
A pyramid on an n sided polygon has ______ faces.
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n+1
Q26Fill in the blanks
If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid is ______.
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30
Q27Fill in the blanks
The given net can be folded to make a ______.
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Prism
Q28Fill in the blanks
A solid figure with only 1 vertex is a ______.
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Cone
Q29Fill in the blanks
Total number of faces in a pyramid which has eight edges is______.
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Five
Q30Fill in the blanks
The net of a rectangular prism has ______ rectangles. (Hint: Every square is a rectangle but every rectangle is not a square.) Three-dimensional figures have three dimensions: length, width and height. A flat surface of a three-dimensional figure is a face. An edge is where two faces meet. A polyhedron is a three-dimensional figure whose faces are all polygons. A vertex of a polyhedron is a point where three or more edges meet. The face that is used to name a polyhedron is called a base.
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Six
Q31Fill in the blanks
In a three-dimensional shape, diagonal is a line segment that joins two vertices that do not lie on the ______ face.
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Same
Q32Fill in the blanks
If 4 km on a map is represented by 1 cm, then 16 km is represented by ______ cm.
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4
Q33Fill in the blanks
If actual distance between two places A and B is 110 km and it is represented on a map by 25 mm. Then the scale used is ______.
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1:4400000
Q34Fill in the blanks
A pentagonal prism has ______ faces.
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7
Q35Fill in the blanks
If a pyramid has a hexagonal base, then the number of vertices is ______.
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7
Q36Fill in the blanks
is the _______ view of
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top
Q37Fill in the blanks
The number of cubes in are ______.
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eight
Q38Fill in the blanks
If the sum of number of vertices and faces in a polyhedron is 14, then the number of edges in that shape is ______.
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12
Q39Fill in the blanks
Total number of regular polyhedra is ______. A prism has two bases, and a pyramid has one base. Prisms Pyramids A Prism is a polyhedron that has A pyramid is a polyhedron that two parallel, congruent bases. The has one base. The base can be bases can be any polygon. The any polygon. The other faces are other faces are parallelograms. triangles.
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Five
Q40Fill in the blanks
A regular polyhedron is a solid made up of ______ faces.
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Congruent
Q41Multiple choice
For each of the following solids, identify the front, side and top views and write it in the space provided.
- (a)
- (b)The faces are all polygons, so the figure is a polyhedron. There is one triangular base. The figure is a triangular pyramid. The faces are not all polygons, so the figure is not a polyhedron. There are two circular bases. The figure is a cylinder. The faces are not all polygons, so the figure is not a polyhedron. There is one circular base. The figure is a cone.
- (c)
- (d)In each of the questions 42 to 61, state whether the following statements are true (T) or false (F).
Show answer
(a)
(b) The faces are all polygons, so the figure is a polyhedron. There is one triangular base. The figure is a triangular pyramid. The faces are not all polygons, so the figure is not a polyhedron. There are two circular bases. The figure is a cylinder. The faces are not all polygons, so the figure is not a polyhedron. There is one circular base. The figure is a cone.
(c)
(d) In each of the questions 42 to 61, state whether the following statements are true (T) or false (F).
Q42Short answer
The other name of cuboid is tetrahedron.
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False
Q43Short answer
A polyhedron can have 3 faces.
Show answer
False
Q44Short answer
A polyhedron with least number of faces is known as a triangular pyramid.
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True
Q45Short answer
Regular octahedron has 8 congruent faces which are isosceles triangles. 1. Explain how to identify a prism or a pyramid. 2. Compare and contrast cylinders and prisms. How are they alike? How are they different? 3. Compare and contrast pyramids and cones. How are they alike? How are they different?
Show answer
False
Q46Short answer
Pentagonal prism has 5 pentagons.
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False
Q47Short answer
Every cylinder has 2 opposite faces as congruent circles, so it is also a prism.
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False
Q48Short answer
Euler’s formula is true for all three-dimensional shapes.
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False
Q49Short answer
A polyhedron can have 10 faces, 20 edges and 15 vertices.
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False
Q50Short answer
The top view of
Show answer
True
Q51Short answer
The number of edges in a parallelogram is 4.
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False
Q52Short answer
Every solid shape has a unique net.
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False
Q53Short answer
Pyramids do not have a diagonal.
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True
Q54Short answer
The given shape is a cylinder.
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False
Q55Short answer
A cuboid has atleast 4 diagonals.
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True
Q56Short answer
All cubes are prisms. Cylinders and cones are not polyhedrons because they are not made of faces that are all polygons. Cylinders Cones A cylinder has two parallel, A cone has one base that is a circle congruent bases that are circles. and a surface that comes to a point called the vertex.
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True
Q57Short answer
A cylinder is a 3-D shape having two circular faces of different radii.
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False
Q58Short answer
On the basis of the given figure, the length of a rectangle in the net of a cylinder is same as circumference of circles in its net.
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True
Q59Short answer
If a length of 100 m is represented on a map by 1 cm, then the actual distance corresponding to 2 cm is 200 m.
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True
Q60Short answer
The model of a ship shown is of height 3.5 cm. The actual height of the ship is 210 cm if the scale chosen is 1: 60.
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True
Q61Short answer
The actual width of a store room is 280 cm. If the scale chosen to make its drawing is 1:7, then the width of the room in the drawing will be 40 cm. Find the volume of each prism. 1. 2. 3.
Show answer
True
Q62Multiple choice
Complete the table given below: S. Solid Shape of Number Number Number F+V E+2 No Solid of faces F of Vertices V of edges E
- a.Cuboid
- b.Triangular Pyramid
- c.Square Pyramid
- d.Rectangular Pyramid e. Pentagonal Pyramid f. Hexagonal Pyramid g. Triangular Prism h. Square Prism i. Cube j. Pentagonal Prism k. Octagonal Prism l. Heptagonal Prism
Show answer
a. Cuboid
b. Triangular Pyramid
c. Square Pyramid
d. Rectangular Pyramid e. Pentagonal Pyramid f. Hexagonal Pyramid g. Triangular Prism h. Square Prism i. Cube j. Pentagonal Prism k. Octagonal Prism l. Heptagonal Prism
Q63Multiple choice
How many faces does each of the following solids, have?
- (a)Tetrahedron
- (b)Hexahedron
- (c)Octagonal Pyramid
- (d)Octahedron
Show answer
(a) Tetrahedron
(b) Hexahedron
(c) Octagonal Pyramid
(d) Octahedron
Q64Short answer
Draw a prism with its base as regular hexagon with one of its face facing you. Now draw the top view, front view and side view of this solid.
Q65Multiple choice
How many vertices does each of the following solids have?
- (a)Cone
- (b)Cylinder
- (c)Sphere
- (d)Octagonal Pyramid (e) Tetrahedron (f) Hexagonal Prism
Show answer
(a) Cone
(b) Cylinder
(c) Sphere
(d) Octagonal Pyramid (e) Tetrahedron (f) Hexagonal Prism
Q66Multiple choice
How many edges does each of following solids have?
- (a)Cone
- (b)Cylinder
- (c)Sphere
- (d)Octagonal Pyramid (e) Hexagonal Prism (f) Kaleidoscope The volume of a three-dimensional figure is the number of cubes it can hold. One cube represents one cubic unit of volume. 1. Use centimetre cubes to build the rectangular prism shown. What are the length, width and height of the prism? How many cubes does the prism hold? 2. You can find out how many cubes the prism holds without counting every cube. First look at the prism from above. How can you find the number of cubes in the top layer without counting every cube? Top 3. Now look at the prism from the side. How many layers does the prism have? How can you use this to find the total number of cubes in the prism? Side 1. Describe a shortcut for finding the number of cubes in a rectangular prism. 2. Suppose you know the area of the base of a prism and the height of the prism. How can you find the prism’s volume? 3. Let the area of the base of a prism be B and the height of the prism be h. Write a formula for the prism’s volume V.
Show answer
(a) Cone
(b) Cylinder
(c) Sphere
(d) Octagonal Pyramid (e) Hexagonal Prism (f) Kaleidoscope The volume of a three-dimensional figure is the number of cubes it can hold. One cube represents one cubic unit of volume. 1. Use centimetre cubes to build the rectangular prism shown. What are the length, width and height of the prism? How many cubes does the prism hold? 2. You can find out how many cubes the prism holds without counting every cube. First look at the prism from above. How can you find the number of cubes in the top layer without counting every cube? Top 3. Now look at the prism from the side. How many layers does the prism have? How can you use this to find the total number of cubes in the prism? Side 1. Describe a shortcut for finding the number of cubes in a rectangular prism. 2. Suppose you know the area of the base of a prism and the height of the prism. How can you find the prism’s volume? 3. Let the area of the base of a prism be B and the height of the prism be h. Write a formula for the prism’s volume V.
Q67Multiple choice
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
- (a)
- (b)
- (c)
- (d)(e) (f) (g) (h) (i) (j) (k) (l) (m) Find the volume of each cylinder. Use 3.14 for π and round to the nearest tenth. 1. 2. 3. 1. Use a similar process to that in earlier Activity to develop the formula for the volume of a cylinder. You will need an empty can or other cylindrical pot. Remove one of the bases. 2. Arrange centimetre cubes in a single layer at the bottom of the cylinder. Fit as many cubes into the layer as possible. How many cubes are in this layer? 3. To find how many layers of cubes would fit in the cylinder, make a stack of cubes along the inside of the cylinder. How many layers would fit in the cylinder? 4. How can you use what you know to find the approximate number of cubes that would fit in the cylinder?
Show answer
(c)
Q68Multiple choice
Count the number of cubes in the given shapes.
- (a)
- (b)
- (c)
- (d)(e) (f) (g) (h) (i) (j) (k) (l) 1. Suppose you know the area of the base of a cylinder and the height of the cylinder. How can you find the cylinder’s volume? 2. Let the area of the base of a cylinder be B and the height of the cylinder be h. Write a formula for the cylinder’s volume V. 3. The base of a cylinder is a circle with radius r. How can you find the area of the base? How can you use this in your formula for the volume of a cylinder?
Show answer
(a)
(b)
(c)
(d) (e) (f) (g) (h) (i) (j) (k) (l) 1. Suppose you know the area of the base of a cylinder and the height of the cylinder. How can you find the cylinder’s volume? 2. Let the area of the base of a cylinder be B and the height of the cylinder be h. Write a formula for the cylinder’s volume V. 3. The base of a cylinder is a circle with radius r. How can you find the area of the base? How can you use this in your formula for the volume of a cylinder?
Q69Multiple choice
Draw the front, side and top view of the given shapes.
- (a)
- (b)
- (c)
- (d)(e) (f) (g) (h) (i) (j) 1. Use a net to construct a rectangular prism that is 3 cm by 6 cm by 9 cm. 2. Use a net to construct a cylinder with a height of 3 cm and a radius of 1.5 cm (Hint: The length of the rectangle in the net must match the circumference of the circles, so the length should be 2π r = 2π (1.5) ≈ 9.42 cm.) A net is a pattern of two-dimensions that can be folded to make a three- dimensional figure. You can use 1 cm graph paper to help you make nets. 1. Use a net to construct a rectangular prism. a. Draw the net at right on a piece of graph paper. Each rectangle is 10 squares by 4 squares. The two squares are 4 small squares on each side. b. Cut out the net. Fold the net along the edges of each rectangle to make a rectangular prism. Tape the edges to hold them in place. 2. Use a net to construct a cylinder. a. Draw the net at right on a piece of graph paper. The rectangle is 25 squares by 8 squares. Use a compass to make the circles. Each circle has a radius of 4 squares. b. Cut out the net. Fold the net as shown to make a cylinder. Tape the edges to hold them in place.
Show answer
(a)
(b)
(c)
(d) (e) (f) (g) (h) (i) (j) 1. Use a net to construct a rectangular prism that is 3 cm by 6 cm by 9 cm. 2. Use a net to construct a cylinder with a height of 3 cm and a radius of 1.5 cm (Hint: The length of the rectangle in the net must match the circumference of the circles, so the length should be 2π r = 2π (1.5) ≈ 9.42 cm.) A net is a pattern of two-dimensions that can be folded to make a three- dimensional figure. You can use 1 cm graph paper to help you make nets. 1. Use a net to construct a rectangular prism. a. Draw the net at right on a piece of graph paper. Each rectangle is 10 squares by 4 squares. The two squares are 4 small squares on each side. b. Cut out the net. Fold the net along the edges of each rectangle to make a rectangular prism. Tape the edges to hold them in place. 2. Use a net to construct a cylinder. a. Draw the net at right on a piece of graph paper. The rectangle is 25 squares by 8 squares. Use a compass to make the circles. Each circle has a radius of 4 squares. b. Cut out the net. Fold the net as shown to make a cylinder. Tape the edges to hold them in place.
Q70Multiple choice
Using Euler’s formula, find the value of unknown x, y, z, p, q, r, in the following table.
- (i)
- (ii)
- (iii)
- (iv)(v) (vi) Faces 7 y 9 p 6 8 Vertices 10 12 z 6 q 11 Edges x 18 16 12 12 r 1. What are the dimensions, in inches, of the rectangular prism that you built? 2. What is the height, in cm, of the cylinder that you built? What is the cylinder’s radius?
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x = 15 y=8 z=9 p=8 q=8 r = 17
Q71Short answer
Can a polyhedron have V = F = 9 and E = 16 ? If yes, draw its figure.
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Yes, draw an octagonal pyramid.
Q72Short answer
Check whether a polyhedron can have V = 12, E = 6 and F = 8.
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No.
Q73Short answer
A polyhedron has 60 edges and 40 vertices. Find the number of its faces.
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22
Q74Short answer
Find the number of faces in the given shapes:
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(a) 14 (b) 10 (c) 16
Q75Short answer
A polyhedron has 20 faces and 12 vertices. Find the edges of the polyhedron.
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30
Q76Short answer
A solid has forty faces and, sixty edges. Find the number of vertices of the solid.
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22
Q77Short answer
Draw the net of a regular hexahedron with side 3 cm. (Hint: Regular hexahedron - cube)
Q78Short answer
Draw the net of a regular tetrahedron with side 6 cm.
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Q79Long answer
Draw the net of the following cuboid: 1. Tell whether a figure’s surface area has increased or decreased if each dimension of the figure is changed by a factor of . 2. Explain how the surface area of a figure is changed if each dimension is multiplied by a factor of 3. 3. Explain how the volume of a figure is changed if each dimension is multiplied by a factor of 2.
Q80Multiple choice
Match the following: Figure Name
- (a)(a) Hexahedron
- (b)(b) Hexagonal Prism
- (c)(c) Square Pyramid
- (d)(d) Cone
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(a) (a) Hexahedron
(b) (b) Hexagonal Prism
(d) (d) Cone
(c) (c) Square Pyramid
Q81Long answer
Complete the table given below by putting tick mark across the respective property found in the solids mentioned. Solids Properties Cone Cylinder Prism Pyramid 1. The figure is a Polyhedron. 2. The figure has diagonals. 3. The shape has curved edges 4. The base of figure is a polygon. 5. The bases are congruent 6. The base of figure is a polygon and other faces meet at a single point. 7. The base of figure is a curved edge and other faces meet at a single point.
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1. Prism, Pyramid 2. Pyramid 3. Cone, Cylinder 4. Prism, Pyramid 5. Cylinder, Prism 6. Pyramid 7. Cone
Q82Short answer
Draw the net of the following shape.
Q83Short answer
Draw the net of the following solid. (Hint: Pentagons are not congruent.)
Q84Short answer
Find the number of cubes in the base layer of the following figure.
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7
Q85Short answer
In the above figure, if only the shaded cubes are visible from the top, draw the base layer.
Q86Short answer
How many faces, edges and vertices does a pyramid have with n sided polygon as its base?
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F = n+1 V = n+1 E = 2n
Q87Short answer
Draw a figure that represents your mathematics textbook. What is the name of this figure? Is it a prism?
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It is a cuboid. Yes.
Q88Short answer
In the given figures, identify the different shapes involved.
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a) Cylindrical mounted by hemi sphere. b) Hexagonal prism mounted by a cone.
Q89Short answer
What figure is formed if only the height of a cube is increased or decreased?
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Cuboid
Q90Multiple choice
Use isometric dot paper to draw each figure.
- (a)A tetrahedron.
- (b)A rectangular prism with length 4 units, width 2 units and height 2 units.
Q91Multiple choice
Identify the nets given below and mention the name of the corresponding solid in the space provided. Nets Name of Solid
- (a)
- (b)
- (c)
- (d)(e) (f)
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(a)
(b)
(c)
(d) (e) (f)
Q92Short answer
Draw a map of your school playground. Mark all necessary places like 2 library, Playground, Medical Room, Classrooms, Assembly area, etc.
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a) 2.1 acre b) Govt Model School I and II c) Park A d) B block e) 6
Q93Multiple choice
Refer to the given map to answer the following questions.
- (a)What is the built-up area of Govt. Model School I ?
- (b)Name the schools shown in the picture.
- (c)Which park is nearest to the dispensary?
- (d)To which block does the main market belong? (e) How many parks have been represented in the map?
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(a) What is the built-up area of Govt. Model School I ?
(b) Name the schools shown in the picture.
(c) Which park is nearest to the dispensary?
Q94Multiple choice
Look at the map given below. Answer the following questions.
- (a)Which two hospitals are opposite to each other?
- (b)A person residing at Niti Bagh has to go to Chirag Delhi after dropping her daughter at Asiad Tower. Mention the important landmarks he will pass alongwith the roads taken.
- (c)Name of which road is similar to the name of some month. B Town, India Sector 26 15 20 Sector 27 1 2 3 4 5 a 17 18 19 14 Flower Road 6 13 Police Fire t Stadium Station 7 Station 16 8 9 12 Sneha Marg 3 11 4 5 6 Sector 20 1 2 3 College 7 8 9 10 School 16 15 14 13 4 Mall Road 10 11 12 5 Sector 19 9 8 7 6 el 5 Sports Nicolson Road Complex Bank 1 (A) 1 2 3 4
Q95Multiple choice
Look at the map given below. Houses B Town, India Sector 26 15 20 Sector 27 1 2 3 4 5 a 17 18 19 14 Flower Road 6 13 Police Fire t Stadium Station 7 Station 16 8 9 12 Sneha Marg 3 11 4 5 6 Sector 20 1 2 3 College 7 8 9 10 School 16 15 14 13 4 Mall Road 10 11 12 5 Sector 19 9 8 7 6 l M 5 Sports Nicolson Road Complex Bank 1
- (A)1 2 3 4 Now answer the following questions. (a) Name the roads that meet at round about.
- (b)What is the address of the stadium?
- (c)On which road is the Police Station situated?
- (d)If Ritika stays adjacent to bank and you have to send her a card, what address will you write? (e) Which sector has maximum number of houses? (f) In which sector is Fire Station located? (g) In the map, how many sectors have been shown?
Q96Short answer
A photographer uses a computer program to enlarge a photograph. What is the scale according to which the width has enlarged?
Q97Short answer
The side of a square board is 50 cm. A student has to draw its image in her notebook. If the drawing of the square board in the notebook has perimeter of 40 cm, then by which scale the figure has been drawn?
Q98Short answer
The distance between school and house of a girl is given by 5 cm in a picture, using the scale 1 cm : 5 km. Find the actual distance between the two places?
Q99Short answer
Use a ruler to measure the distance in cm between the places joined by dotted lines. If the map has been drawn using the scale 1 cm :10 km, find the actual distances between (1) School and Library (2) College and Complex (3) House and School
Q100Short answer
The actual length of a painting was 2 m. What is its length in the photograph if the scale used is 1 mm : 20 cm.
Q101Multiple choice
Find the scale.
- (a)Actual size 12 m Drawing size 3 cm
- (b)Actual size 45 feet Drawing size 5 inches
Q102Multiple choice
In a town, an ice cream parlour has displayed an ice cream sculpture of height 360 cm. The parlour claims that these ice creams and the sculpture are in the scale 1:30. What is the height of the ice creams served? Activity 1 : Find the most appropriate way to reach from start to finish. (Use a coloured pen of your choice to show the path traced.) Start Finish Start Finish Activity 2 : Rohit is a 7 year old young boy. His uncle Raj asked him to draw a map to reach Sport’s Complex from his (Rohit’s) house. He drew the following map. Can you help Uncle Raj by drawing a better map considering yourself as Rohit’s Father/Mother. Activity 3 : Look at the map of city given on the next page:
- (a)Colour the map using the given colour code as follows. Blue-water, Red-Fire station, White-Hospital, Green- Parks, Cream-River Bed, Brown-Mountains.
- (b)Mark the shortest route from House to Pool with the help of arrowes.
- (c)Put X at the intersection of Chatra Marg and House Lane. School Chatra Marg Health Lane Fire Station Pool Lake Street Main Street Home Library Park Hospital House Lane River Lane Sand River Activity 4 : Draw the nets given below on coloured sheets by taking each side of the triangle as 3cm, and try to form the shapes shown in front of it. Count the number of edges, faces and vertices in ends and verify the Euler’s formula. (a) 4 equilateral triangles (b) (c)
- (d)2 squares and 8 triangles (e) 2 pentagons and 10 triangles (f) 6 squares and 8 triangles (g) Activity 5 : Guess who am I? My name is given in the box below. Oops! Spelling of my name is jumbled up. Try to identify it from the clues given below and write it in the blank space. (1) I am a polyhedron with least number of faces. ________ (2) I am a prism whose all faces are square. ________ (3) Looks like marbles but have no vertex. ________ (4) I am a solid whose base is polygonal and other faces are triangles. ________ 6. Draw the map of your locality, showing the details of your sector/ block. Also highlight the appropriate landmarks which will help your friend to locate your house in your sector/block. Activity 7 : Crossword Puzzle Answer the following based on the hints given below. Across 1. Polyhedron whose lateral faces are parallelograms. 2. Prism having fifteen edges. 5. Another name for a square prism. 7. Polyhedron made up of four triangles. 9. Polyhedron made up of convex polygons. Down 2. Polyhedron whose lateral faces are triangles. 3. In a solid shape, the line segment joining two vertices not lying on the same face. 4. A 3-D shape having no vertex. 6. A solid figure having only one vertex. 7. Number of pentagons in a pentagonal prism. 10. Point where edges of a solid shape meet. UNIT-6 3. 2. 1. 4. 6. 10. 5. 7. 8. VISUALISING SOLID SHAPES 211 MATHEMATICS Rough Work