Question

A rock is 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 3 feet per minute. Find the rate at which the area is changing at the instant the radius is 4 feet.

Answer 1

The rate of change of area when radius = 4feet is 75.36 feet²/min.

What is area?

Area definition, any particular extent of space or surface.

Area of circle = πr²

Let the area of the circle be πr²

dr/dt = 3feet/min (GIVEN)

Differentiating both sides with respect to time:

A = πr²

dA/dt =  π(2r).(dr/dt)

dA/dt = (2 * 3.14 * r).(dr/dt)

The rate of change of area when radius = 4feet

dA/dt  = (2 * 3.14 * 4).(3)

dA/dt = 75.36

Hence, the rate of change of area is 75.36feet²/min.

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