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If the area of a circle is decreased by 36%,then the percentage decrease in its perimeter is
- A6%
- B64%
- C36%
- D20%
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CCommunity
Initial Area of a circle, A = π r2, where r is the radius.
New area, A’ = A - 36% A = 64%A = 0.64 A
∴ A’/A = 0.64 ⇒ (r’/r)2 = 0.64 ⇒ r’/r = 0.8 ⇒ r’ = 0.8 r
∴ New perimeter, P = 2πr’ = 2π (0.8)r = 0.8(2πr) = 0.8 P
∴ percentage decrease in perimeter is
$(\frac{{P - P'}}{P} \times 100 = 0.2 \times 100 = 20\% )$
New area, A’ = A - 36% A = 64%A = 0.64 A
∴ A’/A = 0.64 ⇒ (r’/r)2 = 0.64 ⇒ r’/r = 0.8 ⇒ r’ = 0.8 r
∴ New perimeter, P = 2πr’ = 2π (0.8)r = 0.8(2πr) = 0.8 P
∴ percentage decrease in perimeter is
$(\frac{{P - P'}}{P} \times 100 = 0.2 \times 100 = 20\% )$