Chapter 12.2, Problem 36PPS

To determine

To calculate : To find the surface area of given composite solid.

Answer to Problem 36PPS

The required surface area of composite solid is $427.6{\text{in}}^2$

Explanation of Solution

Given information: The composite solid is combination of rectangular prism and a cylinder. The base of rectangular prism is 6 in. by 4 in and the radius of cylinder is 3 in. also height of cylinder is 3 in.

Formula used : The surface area of cylinder is

  $\begin{array}{l}L=2\pi rh\\ S=L+2\pi r^2\end{array}$

Where, L is lateral area.

The surface area of rectangular prism is,

  $\begin{array}{l}L=Ph\\ S=L+2B\end{array}$

Calculation :

For rectangular prism:

  $\begin{array}{l}S=\text{bottom}\text{+}\text{left/right}\text{+}\text{front/back}\\ \text{=}\text{15}\cdot \text{6}\text{+}\text{2}\left(4\cdot 15\right)+2\left(6\cdot 4\right)\\ =90+120+48\\ =258\end{array}$

For half cylinder:

  $\begin{array}{l}S=\frac{2\pi \left(3\right)\left(15\right)+2\pi {\left(3\right)}^2}{2}\\ =\frac{18\pi +90\pi }{2}\\ =54\pi \end{array}$

Total surface area is,

  $\begin{array}{l}258+54\pi \\ =427.6{\text{in}}^2\end{array}$