spherical balloon is being filled with gas from a cylinder. The cylinder has a radius of 9 inches, and
its lid can be compressed so that the cylinder height decreases, reducing the volume of the cylinder
and forcing gas directly into the balloon. As a reminder, the volume of a cylinder is π(radius)2height,
and the volume of a sphere is 4
3 π(radius)3.
At the moment that the balloon’s radius is 3 inches, that radius is increasing at a rate of 5 inches per
minute.
(a) At that moment, at what rate is the volume of the balloon increasing?
(b) At that same moment, at what rate is the lid of the cylinder moving downward? (Remember
that any increase in the balloon’s volume is the result of an identical decrease in the cylinder’s
volume.