The radius of a sphere is increasing at a rate of 2 inches per minute. Find the rate of change of the volume of the sphere when the radius is 8 inches.

512π cubic inches/minute

Step-by-step explanation:

Volume V = 4/3 π r^3

dV / dr =   4 π r^2

dr/dt = 2

Rate of change of the Volume:

dV/dt = dV / dr  * dr/dt

= 4 π r^2 * 2

=   8 π r^2

When r = 8:

dV/dt = 8π(8)^2

= 512π cubic inches/minute

true

step-by-step explanation: