Chapter 3.5, Problem 145E

(a)

To determine

To calculate: The height h of a cylindrical metal tank as a function of its radius r which is to hold 500 ${\text{ft}}^3$ of gasoline.

(b)

To determine

To calculate: The surface area S of the cylindrical tank as a function of its radius r, given the relation $h=\frac{500}{\pi r^2}\text{ft}$ and graph this function.

(c)

To determine

The radius to the nearest tenth of a foot of the cylinder which minimizes the surface area of the cylinder using the minimum feature of a graphing calculator, the surface area is given by $S=2\pi r^2+\frac{1000}{r}$ where S is the surface area and r is the radius of cylinder.

(d)

To determine

To calculate:

The minimum cost to make a cylindrical tank, given radius for minimum surface area is $4.3\text{ ft}$, the surface area is given by $S=2\pi r^2+\frac{1000}{r}$ and the cost to make it is $8 per square foot.