Question

If the rate of increase of the radius of a circle is $5cm/s$, then the rate of increase of its area, when the radius is $20cm$, will be

• A. $10\pi$
• B. $20\pi$
• C. $200\pi$
• D. $400\pi$

Answer 1

The correct option is C $200\pi$

Since, area of circle, $A=\pi r^2$
On differentiating with respect to $t$, we get
$\frac{dA}{dt}=2\pi r\frac{dr}{dt}$
$=2\pi \cdot 20\cdot 5=200\pi$