A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.2 cm/min.

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 16 cm. (Note the answer is a positive number).

Answer 1

x = diameter

V = (4/3)πr³ = (4/3)π(x/2)³ = (1/6)πx³

dV/dt = dV/dx dx/dt = (1/2)πx² dx/dt

dV/dt = (1/2)πx² dx/dt

Now plug in

x = 16 cm

dx/dt = -0.2 cm/min (negative because x is decreasing)

and evaluate dV/dt. The answer will come out in cm³/min. Note that dV/dt is the rate of change, and it is negative, so the rate of decease is the absolute value of dV/dt.