Question

A snowball is melting at a rate of 324π mm3/s. At what rate is the radius decreasing when the volume of the snowball is 972π mm3?

Answer 1

Answer:

The radius is decreasing at 4 mm/s

Explanation:

The volume of a sphere is:

$V = 4/3*\pi *r^3$   So, when the volume is 972π mm^3 the radius r is:

r = 9mm

Now, the change rate is given by the derivative:

$dV/dt = 4/3*\pi *3*r^2*dr/dt$  

Where: dV/dt = -324π mm^2/s

            r = 9mm

Solving for dr/dt:

dr/dt = -4mm/s