Question

The diameter of a circle is increasing at the rate of $1$ cm/sec. When its radius is $\pi$ , the rate of increase of its area is

• A. $\pi c{m}^2/sec$
• B. $2\pi c{m}^2/sec$
• C. ${\pi }^{2}c{m}^2/sec$
• D. $2{\pi }^{2}c{m}^2/sec$

Answer 1

Answer: (C)

${\pi }^{2}c{m}^2/sec$

$D=2r$

$\Rightarrow \frac{dD}{dt}=2\frac{dr}{dt}$

$\Rightarrow \frac{dr}{dt}=\frac{1}{2}cm/sec$

Area of circle $A=\pi r^2$

$\Rightarrow \frac{dA}{dt}=2\pi r\frac{dr}{dt}$

$\Rightarrow \frac{dA}{dt}={\pi }^{2}c{m}^2/sec$