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) $-\pi {\mathrm{cm}}^2/\mathrm{s}$
• (B) $10\pi {\mathrm{cm}}^2/\mathrm{s}$
• (C) $0.1\pi {\mathrm{cm}}^2/\mathrm{s}$
• (D) $\pi {\mathrm{cm}}^2/\mathrm{s}$

Answer 1

The Correct Option is D

Explanation:
Given that, $\frac{dr}{dt}=0.1\mathrm{cm}/\mathrm{s}$$\therefore$Area $,A=\pi r^2$On differentiating w.r.t. $t,$ we get $\Rightarrow \frac{dA}{dt}=2\pi r\frac{dr}{dt}$${\therefore \frac{dA}{dt}|}_{r=5}=10\pi \times 0.1=\pi {\mathrm{cm}}^2/\mathrm{s}$