A rectangular sheet of paper is rolled in two different ways to form two different cylinders. Find the volume of cylinders in each case if the sheet measures 44 cm × 33 cm. 1. Rashid has decided to build a swimming pool as shown in the figure on an empty plot 25 metres long and 15 metres wide. He is discussing with his son Majid about his plan to build the pool, put tiles on the bottom of the pool and other requirements of the pool. Can you help Majid to answer the following questions which his father has asked in the discussion? 1. What is the surface area of the pool? 2. If Rashid plans to cover the bottom and sides of the pool with square tiles having side 25 cm, how many such tiles will be required? 3. If each tile costs Rs 40, how much will be the total cost? 4. A local digging company charges at the rate of Rs 150/- per cubic metre. How much Rashid has to pay for digging the swimming pool? [Hint : Volume = base area × height] 5. How long will it take for the swimming pool to be filled completely, if a pipe is pouring water into the pool at the rate of 40 litres per minute? 6. What is the area of the wall at the shallow end of the swimming pool? 7. What is the area of the wall at the deep end of the swimming pool? 8. How much Rashid has to pay in total for making the swimming pool operational, considering cost of digging the pool and fixing tiles? 2. The following table shows the dimensions of cuboids such that, their volumes remain the same. Extend the table with as many more dimensions such that all the cuboids thus formed have the same volume. Complete the table and write your conclusion on surface area and volume of each cuboid. Dimensions of cuboid Surface Area Volume (in units) (sq. unit) (cube unit) 15, 10, 8 1200 6, 10, 20 1200 -- -- -- -- -- -- -- -- -- -- -- -- 3. The figure shown is a geoboard in which a rectangle has been outlined using a rubberband. 1. What is the area of the rectangle? 2. Draw a similar figure whose area is 50% larger than this figure. 3. Draw a similar figure whose area is 25% larger than this figure. 4. Suppose that the figure shown is 75% of another figure. What would the other figure look like? 5. The enclosed area represents 75% of another area on the geoboard. Use a geoboard or draw a diagram of a geoboard to represent 100% of the area. i. Given here are sketches of front, back, sides and roof of a kennel. The drawings are as per the scale. 1 cm = 10 cm. Area 12cm2 Back 3 cm Roof 4 cm 4 cm Front 3 cm Area 12 cm2 Roof 1cm Side 3 cm Base 3 cm 4 cm 3 cm Side 3 cm 3 cm 4 cm 3 cm (ii) Sketches given above belong to which kennel?
- (a)
- (b)
- (c)(iii) Draw the net of the correct choice on the graph paper. (iv) Take a waste piece of cardboard. Trace the net you have drawn above on the cardboard and fold it to make the kennel. (v) If you had to pay Rs 2 for each square cm of surface area, how much would it cost you to paint the kennel? 5. Word Maze r h r h o m b u s z a t h a m o b s u q b t r a p e z i u m c y l i n d e r b c t z w v a m q r e u i j l t q n g b a b k b d f v s g t r o s z q c i r c l e i a w h m a n k p e d Find the names of the solids from the given word maze whose areas or volumes are given below by colouring the boxes using the given colour code. Area/Volume Colour Code 1. d × d2 red 2 1 2. lbh blue 3. πr 2h yellow 4. πr 2 green 5. bh orange 6. (a + b) × h pink