Question

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

Answer 1

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