Find the rate of change of the area of a circle per second when the radius increases at a speed of 2 cm/s and diameter D = 10 cm.
Answer & explanation
Correct answer: option 3
Area of circle, $A=\pi r^2$
$⇒\frac{dA}{dt}=2\pi r\frac{dr}{dt}$
$⇒\frac{dA}{dt}=2\pi×5×2$
$⇒\frac{dA}{dt}=20\pi\,cm^2/s$