Q. The radius of a circular plate is increasing at the rate of 0.01 cm/s when the radius is 12 cm. Then , The rate at which the area increase, is
A) $0.24\ \pi\$sq cm/s
B) $60\ \pi\$sq cm/s
C) $24\ \pi\$sq cm/s
D) $1.2\ \pi\$sq cm/s
Explanation
(a)
The area of circular plate is $A = \pi r^{2}$
$\Rightarrow \ \frac{dA}{dt} = 2\pi r \bullet \frac{dr}{dt}$
$\Rightarrow \ \frac{dA}{dt} = 2\pi(12)(0.01) = 0.24\pi\$sq cm/s
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.