Question

A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.2 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 12 cm. (Note the answer is a positive number).

Answer 1

V = (pi/6)D^3
-dV/dt = -3*(pi/6)*D^2*dD/dt
= -(pi/2)*D^2*dD/dt

The rate of decrease of diameter, dD/dt, is negative, so the answer is positive.

Now, perform the calculation.

Answer 2

45.2389342117