Textbook Problem

Volume The axis of a storage tank in the form of a right circular cylinder is horizontal (see figure). The radius and the length of the tank are 1 meter and 3 meters respectively.

Determine the volume of fluid in the tank as a function of its depth d.

Use a graphing utility to graph the function in part (a).

Design a dip stick for the tank with markings of $\frac{1}{4}$, $\frac{1}{2}$, and $\frac{3}{4}$.

Fluid is entering the tank at a rate of $\frac{1}{4}$ cubic meter per minute. Determine the rate of change of the depth of the fluid as a function of its depth d.

Use a graphing utility to graph the function in part (d). When will the rate of change of the depth be minimum? Does this agree with your intuition? Explain.