Page 248 - Start Up Mathematics_7

Solution: Diameter of the circular flowerbed = 66 m

Radius of the flowerbed (r) = 66 ÷ 2 = 33 m
Radius of the outer circle = R = 33 + 4 = 37 m (Width of path = 4 m)
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Area of the outer circle = πR = π × 37 × 37 = 1,369π
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Area of the circular flowerbed = πr = π × 33 × 33 = 1,089π
Area of the path = Area of outer circle – Area of flowerbed
= 1,369π – 1,089π
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= 280π = 280 × = 880 m 2
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Example 28: A circular flower garden has an area of 314 m . A sprinkler at the centre of the
garden can cover an area that has a radius of 14 m. Will the sprinkler water the entire
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garden? (Take π = )
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Solution: Area of the circular flower garden = 314 m 2
The sprinkler can cover a circular area with radius = 14 m

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∴ Area of the circle covered by the sprinkler = πr = 22 × 14 × 14 = 616 m 2
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Since the area of the circle covered by the sprinkler is more than the area of the flower
2
2
garden (616 m > 314 m ). Therefore, the sprinkler will water the entire garden.
Example 29: Find the circumference of the inner circle shown in the adjoining 7 m
figure? (Take π = 22 )
7 O 21 m
Solution: Radius of the inner circle (r) = 21 m – 7 m = 14 m
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Circumference of the inner circle = 2πr = 2 × × 14 = 88 m
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Example 30: 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 in the same time period? (Take π = 22 )
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Solution: Radius of the circle described by minute hand = 14 cm
Circumference of the circle described by minute hand = 2πR = 2 × 22 × 14 = 88 cm
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1
Distance covered by the tip of minute hand in half an hour = (88) = 44 cm
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Distance covered by the tip of hour hand in half an hour = 1 (2πr)
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1 22 44
= c 2 × × 7m = = 1.83 cm
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Example 31: How many times a wheel of radius 28 cm must rotate to cover 264 m? (Take π = 22 )
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22
Solution: Circumference of the wheel = 2πr = 2 × × 28 = 176 cm ( r = 28 cm)
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Number of times the wheel must rotate = Distance covered
circumferenceofwheel

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