CPM Homework Help : APCALC Problem 7-57

Sam the snowman has a spherical head that is melting at a rate of $12 \text{ in}^3$ per hour. Assume that as it melts, his head remains spherical. What is 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:

$r≈1.954 \text{ _____}$
Be mindful of units.