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Question
There are two circular gardens A and B. The circumference of garden A is 1.760 km and the area of garden B is 25 times the area of garden A. Find the circumference of garden B.
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Solution
Let r be the radius of the circular garden A
Since the circumference of the garden A is 1.760 km = 1760 m, we have,
2πr = 1760 m
⇒ r = `[ 1760 xx 7 ]/[ 2 xx 22 ]` = 280 m
Area of garden A = πr2 = `22/7` x 2802 m2
Let R be the radius of the circular garden B.
Since the area of the garden, B is 25 times the area of garden A, We have,
πR2 = 25 x πr2
⇒ πR2 = 25 x π x 2802
⇒ R2 = 1960000
⇒ R = 1400 m
Thus circumference of garden B = 2πR
= `2 xx 22/7 xx 1400` = 8800 m = 8.8 km.
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