Question

Spherical balloon loses air at pi cubic inch per minute
What is rate of change at 10 inches?
What is the rate of change at 5 inches?

Answer 1

Assuming you want the rate of change of the radius, since we are given the rate of change for the volume ....

V = (4/3)π r^3
dV/dt = 4π r^2 dr/dt
-π = 4π (10^2) dr/dt , -π since it said "loses", so it is decreasing
-1 = 400 dr/dt
dr/dt = -1/400

when the radius is 10 inches, the radius is decreasing at 1/400 inches/minute

repeat for 5 inches