1.

If the area of a circle is decreased by 36%,then the percentage decrease in its perimeter is1). 6%2). 64%3). 36%4). 20%

Answer»

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

$(\frac{{P - P'}}{P} \times 100 = 0.2 \times 100 = 20\% )$



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