Question

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

• A. $-\pi c{m}^2/s$
• B. $10\pi c{m}^2/s$
• C. $0.1\pi c{m}^2/s$
• D. $5\pi c{m}^2/s$
• E. $\pi c{m}^2/s$

Answer 1

The correct option is E

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

Explanation for correct answer

Given,

$\frac{dr}{dt}=0.1cm/sec$

We know that area of circle is

$A=\pi r^2$

On differntiating the area with recpect to radius

$\frac{dA}{dt}=2\pi r\left(\frac{dr}{dt}\right)$

$$\begin{gathered} =2\times 5\times \pi \times 0.1 \\ =\pi c{m}^2/sec \end{gathered}$$

Hence the rate of change of the area of circle is $\pi c{m}^2/s$.

Therefore, option(E) is correct option: