Q. If the radius of a circle be increasing at a uniform rate of 2cm/s. The area of increasing of area of circle ,at the instant when the radius is 20 cm, is
A) $70\pi cm^{2}/s$
B) $70cm^{2}/s$
C) $80\pi cm^{2}/s\$
D) $80\ cm^{2}/s$
Explanation
(c)
Let area of circle,$A = \pi r^{2}$
$\Rightarrow \ \ \ \ \frac{dA}{dt} = 2\pi r\frac{dr}{dt} \Rightarrow \frac{dA}{dt} = 2\pi.20.2$
$\Rightarrow \ \ \ \ \ \frac{dA}{dt} = 80\pi\ cm^{2}/s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.