Q. The radius of a circle is increasing at the rate of 0.1 cm/s. When the radius of the circle is 5 cm, the rate of change of its area, is
A) $- \pi cm^{2}/s$
B) $10\pi cm^{2}/s$
C) $0.1\pi cm^{2}/s$
D) $\pi cm^{2}/s$
Explanation
(d)
Let area, $A = \pi r^{2}$
$\Rightarrow \ \ \ \frac{dA}{dt}2\pi r\frac{dr}{dt}$
$\therefore\ \left. \ \frac{dA}{dt} \right|_{r = 5} = 10\pi \times 0.1 = \pi\frac{cm^{2}}{s}\ \lbrack\because\frac{dr}{dt} = 0.1cm/s\rbrack\$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.