Chapter 12.3, Problem 27PPS

To determine

To find:

The surface area of the tank.

Answer to Problem 27PPS

The total surface area of tank is $\text{266}\pi {\text{ ft}}^2$ .

Explanation of Solution

Given information:

Tank has diameter $\text{14 ft}$ , height is $\text{11 ft}$ and slant height is $9\text{ ft}$ .

Calculation:

Tank is made up of the lateral area of circle, a cone and a cylinder.

Lateral area of circle is when $r=7\text{ ft}$ .

  $\begin{array}{c}{L}_{circle}=\pi r^2\\ =\pi {\left(7\right)}^2\\ =49\pi \end{array}$

Lateral area of cone is:

  $\begin{array}{c}{L}_{cone}=\pi rl\\ =\pi \left(7\right)\left(9\right)\\ =63\pi \end{array}$

Lateral area of cylinder is:

  $\begin{array}{c}{L}_{cylinder}=2\pi rh\\ =2\pi \left(7\right)\left(11\right)\\ =154\pi \end{array}$

So, the total surface area of tank is:

  $\begin{array}{c}S=L_{circ}+L_{cone}+L_{cylinder}\\ =49\pi +63\pi +154\pi \\ =266\pi \end{array}$

Hence, the total surface area of tank is $\text{266}\pi {\text{ ft}}^2$ .