Chapter 12.2, Problem 37PPS

To determine

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

Answer to Problem 37PPS

The required surface area of composite solid is $1059.3{\text{cm}}^2$

Explanation of Solution

Given information: The composite solid is combination of a cube and a cylinder. The length of each side of cube 12 cm and radius of the cylinder is 6 cm. The height of the solid is 12 cm.

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:

  $\begin{array}{l}S=\text{bottom}\text{+}\text{left/right}\text{+}\text{front/back}\\ \text{=}5\left(12\cdot 12\right)\\ =5\left(144\right)\\ =720\end{array}$

For half cylinder:

  $\begin{array}{l}S=\frac{2\pi \left(6\right)\left(12\right)+2\pi {\left(6\right)}^2}{2}\\ =\frac{144\pi +72\pi }{2}\\ =108\pi \end{array}$

Total surface area is,

  $\begin{array}{l}720+108\pi \\ =1059.3{\text{cm}}^2\end{array}$