Page 244 - ICSE Math 7

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Area of the outer circle = pR = p × 37 m × 37 m = 1,369p m 2
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Area of the circular flowerbed = pr = p × 33 m × 33 m = 1,089p m 2
Area of the path = Area of outer circle – Area of flowerbed

= (1,369p – 1,089p)
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2
2
= 280p m = 280 m × = 880 m 2
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Example 20: The minute hand of a circular clock is 14 cm long. How far does the tip of the minute
hand move in 30 minutes? How far does the tip of an hour hand that is 7 cm long, move
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in the same time period? (Take p = )
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Solution: Radius of the circle described by minute hand = 14 cm
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Circumference of the circle described by minute hand = 2pr = 2 × × 14 cm = 88 cm
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1
Distance covered by the tip of minute hand in half an hour = × 88 cm = 44 cm
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1
Distance covered by the tip of hour hand in half an hour = × 2pr
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1 22 44
= 2 × × 7 cm = cm = 1.83 cm
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EXERCISE 21.3

1. Find the circumference of the circles, given that:
(a) radius = 21 mm (b) diameter = 14 cm
2. Find the area of the circles, given that: (a) radius = 20 cm (b) diameter = 42 cm

3. Find the radius of a circle whose circumference is 39.6 cm.

4. Find the ratio of the circumferences of two circles whose radii are in the ratio 4 : 5.
5. The inner circumference of a circular track is 176 m. The track is 7 m wide. Calculate the:
(a) area of the track.

(b) cost of putting up a fence along the outer circle at the rate of ` 12 per metre.
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(Use p = )
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6. The circumference of a circle exceeds its radius by 37 cm. Find the diameter of the circle.
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(Use p = )
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7. The diameter of a wheel of a bus is 112 cm. How many revolutions will it make to cover 1 km
56 metres?
8. The circumferences of two circles are in the ratio 1 : 3. Find the ratio of their areas.
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9. A copper wire in the form of a circle, encloses an area of 616 cm . If the same wire is bent to
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form a square, find its area. (Use p = )
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