Chapter 12.3, Problem 6PSB

To determine

Find the total (including the rectangular face) surface area of a half cylinder.

Answer to Problem 6PSB

  $130\mathrm{s}\mathrm{q}\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}$

Explanation of Solution

Given information:

Radius of $5$ and a height of $2$ .

  

Calculation

It is given that,

  

  $\begin{array}{l}\mathrm{R}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{u}\mathrm{s}=5\\ \mathrm{H}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}=2\end{array}$

Surface area of rectangle,

  $\begin{array}{l}\mathrm{A}\mathrm{r}\mathrm{e}\mathrm{a}\left(\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}2\right)=\mathrm{b}\mathrm{h}\\ =10\times 2\\ =20\mathrm{s}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\end{array}$

  $\begin{array}{l}\mathrm{A}\mathrm{r}\mathrm{e}\mathrm{a}\left(\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}1\&3\right)=\mathrm{\pi }{\mathrm{r}}^2\\ =3.14\times 5^2\\ =78.5\mathrm{s}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\end{array}$

  $\begin{array}{l}\mathrm{A}\mathrm{r}\mathrm{e}\mathrm{a}\left(\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}4\right)=\mathrm{h}\times \frac{1}{2}\mathrm{C}\\ =2\times \frac{1}{2}\times 10\mathrm{\pi }\left[\therefore \mathrm{C}=2\mathrm{\pi }\mathrm{r}=10\mathrm{\pi }\right]\\ =31.4\mathrm{s}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\end{array}$

Total Area,

  $\begin{array}{l}78.5+31.4+20\\ =130\mathrm{s}\mathrm{q}\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\end{array}$

Hence, total area is $130\mathrm{s}\mathrm{q}\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}$ .