Question

A rock it thrown into a still pond. The circular ripples move outward from the point of impact of the rock so that the radius of the circle formed by a ripple increases at the rate of 4 feet per minute. Find the rate at which the area is changing at the instant the radius is 18 feet.

Answer 1

The area depends on the radius so we can write A=πr².

Differentiate this wrt time: dA/dt=2πrdr/dt.

dr/dt is the rate of change of the radius=4 (ft/min) while dA/dt is the rate of change of the area.

Therefore, when r=18, dA/dt=2π(18)(4)=144π sq ft/min=452.39 sq ft/min approx.