Q106Multiple choice
The students of Anju’s class sold posters to raise money. Anju wanted to create a ratio for finding the amount of money her class would make for different numbers of posters sold. She knew they could raise Rs 250 for every 60 posters sold.
- (a)How much money would Anju’s class make for selling 102 posters?
- (b)Could Anju’s class raise exactly Rs 2,000? If so, how many posters would they need to sell? If not, why? Distance Travelled 1. Speed = Time Taken Calculate the speed for at least 10 students of your class by giving them a certain distance to walk. Measure the distance each student has walked and record the time taken by each to cover the distance. Then, complete the table given below: Name of the Distance walked Time taken Rate of speed student (in metres) (in minutes) (in m/min) Which student ran the fastest? 2. Figures that have the same shape but not necessarily the same size are called similar figures. We can make rectangles with similar figures by increasing or decreasing its dimensions in the same ratio. Let us make similar figures using square tiles. What is the length of a similar rectangle where width is made up of 12 tiles? Let us consider a rectangle having 10 square tiles along the length and 4 along the breadth as shown in the figure. 10 10 4 4 Use tiles to make a 10 × 4 rectangles. Add tiles to increase width of 4 the rectangle to 12 tiles. The width of the new rectangle is three times the width of the original rectangle. To keep the ratios of the lengths of two rectangles proportional, the length of this new rectangle must also be three times the length of the original rectangle. Add tiles to increase the length of the rectangle to 30 tiles. To check our answers, we can use the idea of direct proportion. 4 12 = 10 30 2 2 or, = 5 5 Do yourself Use square tiles to make similar rectangles with given dimensions and find x. (a) The original rectangle is 8 tiles wide and 6 tiles long. The similar rectangle is 16 tiles wide and x tiles long. (b) The original rectangle is 3 tiles wide and 7 tiles long. The similar rectangle is 9 tiles wide and x tiles long. 3 Inverse Variation Take four cylindrical containers of the same size each of radius 5 cm. Fill the containers with different types of liquids with same mass (different density) like Mercury, Water, Alcohol, Oil. Note the height in each case at which the level of liquid stands. Tabulate this information in the following table and show that this is case of inverse proportion. Density Mercury Water Alcohol Oil (g/cm3) 13.6 (D1) .99 (D2) .78 (D3) .96 (D4) Height (cm) H1 H2 H3 H4 Density × Height = Constant. 4. Crossword Across 1. Two things are said to be varying __________ if they increase (decrease) together such that ratio of their corresponding values remains constant. 4. Problems based on direct proportion can be solved using __________ method. 5. More the number of workers, ___________ the number of days to finish a job. 7. Indirect ___________. 9. Two quantities are said to be in inverse proportion if an increase in one quantity causes a proportional ___________ in other. Down 2. Speed and time are in ____________ proportion to each other if distance remains the same. 3. It is used to compare two ratios or make __________ fractions. 6. ‘k’ is called _________ of variation. 7. In inverse proportion, ___________ of corresponding values remains constant. 8. With an increase in quantity of milk, cost of milk also ___________. MATHEMATICS UNIT-10 Rough Work DIRECT AND INVERSE PROPORTIONS 335 MATHEMATICS Rough Work
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