A circle is expanding. If the radius is changing at a rate of 4, find the rate of change of the area when the radius is 1.

Question

A circle is expanding. If the radius is changing at a rate of 4, find the rate of change of the area when the radius is 1.

Answer 1

The equation for the area of a circle in terms of the radius is A = πr² or A(r) = πr²

Now, differentiate both sides with respect to time (to get a rate).

Use the chain rule:

You are given dr/dt = 4 and r = 1 so:

dA/dt = 2π(1)(4) = 8π (since no units are given, I can't provide unots for the answer)