**Problem 28**

A water tank, open at the top, consists of a right circular cylinder and a right circular cone, as shown. If the altitude of the cylinder is three times its radius, and the altitude of the cone is two times the same radius, find the number of square feet of sheet metal required to construct a tank having a capacity of 10,000 gal. (One gal. = 231 cu. in.)

**Solution 28**

$V = 1336.806 ~ \text{ft.}^3$

$V_{cylinder} + V_{cone} = V$

$\pi r^2 h_1 + \frac{1}{3}\pi r^2 h_2 = V$

$\pi r^2(3r) + \frac{1}{3}\pi r^2(2r) = 1336.806$

$\frac{11}{3}\pi r^3 = 1336.806$

$r = 4.878 \, \text{ft.}$

$h_1 = 3(4.878) = 14.634 ~ \text{ft.}$

$h_2 = 2(4.878) = 9.756 ~ \text{ft.}$

$A = A_{L-cylinder} + A_{L-cone}$

$A = 2\pi rh_1 + \pi rL$

$A = 2\pi(4.878)(14.634) + \pi(4.878)\sqrt{4.878^2 + 9.756^2}$

$A = 615.68 ~ \text{ft.}^2$ *answer*