CPM Homework Help : CALC Problem 7-61

Sam the snowman has a spherical head that is melting at a rate of $12$ in^{$^{3}$} per hour. Assume that as it melts, it remains spherical. Find the radius of Sam's head when the radius is changing at $0.25$ inches per hour.

Hint:

$V=\frac{4}{3}\pi r^{3}$
How can you construct an equation that describes how the volume of Sam's head is changing over time?

More Help:

$\frac{dV}{dt}=-12, \ \ \ \frac{dr}{dt}=-0.25$

Answer:

$r ≈ 1.954$ _____
Be mindful of units.