You are baking perfectly cylindrical cookies whose radius is 3 times the height throughout the

baking process. You also know that the volume of a cylinder of radius r and height h is V = pr2h

in appropriate units.

(a) The recipe is written by an eccentric mathematician and instructs you to bake

until each cookie is expanding in volume at a rate of 36p cubic millimeters per minute and

in height at a rate of 1

12 millimeters per minute. Your oven only allows you to look at the

height of the cookies. At what cookie height should you stop baking?

(b) You get distracted and are 7.20 seconds (= 12

100 minutes) late in stopping. Using

linear approximation, what is the approximate height of each cookie?