The radius r of a circle is increasing at a rate of 3 inches per minute. Find the rate of change of the area when r = 5 inches and r = 21 inches. (a) r = 5 inches

A=πr²

dA/dt=dA/dr*dr/dt

dA/dr=2πr

dA/dt=2πr dr/dt

we are told that the radius is increasing at the rate 3 in/min

dr/dt=3 in/min

we are required to find:

a] (dA/dt) when radius is r=5 inch

dA/dt=2πr dr/dt

dA/dt=2π (5) * 3

dA/dt=30π in² / min

b] (dA/dt) when radius is r=21 in

dA/dt=2πr dr/dt

dA/dt=2π (21) * 3

dA/dt=126π in²/min