Question

General Application of Derivatives. Draw the necessary figure and indicate the dimension given.

1. If the radius of the circle increases at the rate of 0.01 cm per second, find the rate of change of the area when the radius is 3 cm long.

Answer 1

$A=\pi r^2\\ \frac{dA}{dr}=2\pi r\\ \frac{dA}{dt}=\frac{dA}{dr}×\frac{dr}{dt}\\ \frac{dA}{dt}=2\pi r × 0.01\\ \frac{dA}{dt}=0.06\pi$