The radius of a circle is increasing at a rate of 4 ft/min. At what rate is its area changing when the radius is 2 ft? (Recall that for a circle, A = 𝜋r2.) ______ ft2/min

Question

The radius of a circle is increasing at a rate of 4 ft/min. At what rate is its area changing when the radius is 2 ft? (Recall that for a circle, A = 𝜋r².)

 

_________ ft²/min

Answer 1

We know A = pi*(radius)^2

We know dr/dt and want dA/dt

So take the derivative of the first equation with respect to time:

dA/dt = 2 * pi * r * dr/dt

Now plug in r = 2 and dr/dt = 4

so dA/dt = 2*pi*2*4 = 16*pi

Answer 2

A = πr²

dA / dt = 2πr(dr / dt) = 2π(2 ft)(4 ft / min) = 16π ft² / min