Page 156 - Start Up Mathematics_8 (Non CCE)

3. Complete the following tables assuming that x is in direct variation with y:

(a) x 60 ... 180 ... ... ... (b) x ... 9 ... 15 ... 26.5

y 4 8 12 15 20 25 y 3.5 4.5 6.5 ... 9.25 ...
4. Vicky bought 15 notebooks for ` 240. How many notebooks can he buy for ` 160?
5. Arushi takes 130 minutes to walk a distance of 110 metres. How much time will she take to walk a
distance of 275 metres?
6. A train is moving at an average speed of 70 km/h. How much distance will it cover in 25 minutes?
7. On a particular day, 150 US dollars are worth ` 7,425. On the same day, what will be the worth of
250 US dollars?
8. If 5 men or 8 women earn ` 625 per day, how much would 8 men and 12 women earn per day?
9. A worker is paid ` 240 for 5 days work. If his total income is ` 1,008, for how many days did he
work?
10. The amount of extension in an elastic string is in direct variation with the weight hung on it. If a weight
of 250 g produces an extension of 3.5 cm, then what weight would produce an extension of 21 cm?
11. The thickness of 12 sheets of chart papers is 35 mm. What is the thickness of 294 sheets of chart
papers?
8
12. In 12 days, the earth picks up 1.8 × 10 kg of dust from the atmosphere. In how many days will it
8
pick up 7.2 × 10 kg of dust?
2
2
13. 35 children need 122.5 m of space for a dance performance. If the available space is 21 m , how
many children can give the performance?

MATHS LAB ACTIVITY

Objective: To deduce a direct variation
Material required: Art sheet, coloured sheets of paper, glue stick or fevicol, geometry box
Procedure:
Step 1: Cut six circles of different radii from coloured sheets and paste them on the art sheet.
Step 2: By sliding the ruler on the circles, mark and measure the longest chord, i.e., the diameter
of the circle.
2
Step 3: Using the formula, Area of circle = pr , record areas of all the circles in the given table:
Can you deduce a direct variation between the radius (r) and area of circle (A)?
r
Step 4: Check if is a constant.
A Radius (r)
Step 5: Write all the steps on the art sheet. (in cm)
Area of circle (A)
2
Result: What can you conclude from this? (in cm )

Inverse variation
If two quantities x and y vary in such a manner that xy is constant and positive, then x and y are said to be in
inverse variation. In other words, x and y are in inverse variation if xy is always constant. This constant is
the constant of variation (say k).
Ê 1ˆ
xy = k or x = k Á ˜
y¯
Ë
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