Answer to Question #155232 in Calculus for Rachel

Question

A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.3 cm/min. At what rate is the volume of the snowball decreasing when the radius is 9 cm. (Note the answer is a positive number).

Answer 1

Sphere V = ⁴/₃πr³

dV/dr = 3(⁴/₃πr²) = 4πr²

dr/dt = 0.3 cm/min

dV/dt = (dV/dr)(dr/dt) = (4πr²)(0.3) = 1.2πr²

dV/dt (r = 9) = 1.2π9² = 305 cm³/min