Question

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

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

Answer 1

Answer: (C)

Since, area of circle, $A=\pi r^{2}$

On differentiating w.r.t. t, we get

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

$=2\pi\cdot20\cdot5=200\pi$