The radius of a circle is increasing at the rate of 0.1 cm/s... | Mathematics | SolveeIt | Solveeit

Today, August 19

Question

The radius of a circle is increasing at the rate of 0.1 cm/s. When the radius of the circle is 5 cm, the rate of change of its area is

A

(A) −πcm2/s

B

(B) 10πcm2/s

C

(C) 0.1πcm2/s

D

(D) πcm2/s

Answer

(D) πcm2/s

Explanation

Solution

Explanation:
Given that, drdt=0.1cm/s∴Area ,A=πr2On differentiating w.r.t. t, we get ⇒dAdt=2πrdrdt∴dAdt|r=5=10π×0.1=πcm2/s