Chapter 12, Problem 6PT

To determine

To calculate : The lateral area and surface area.

Answer to Problem 6PT

The lateral area $L=619.7f{t}^2$ and the surface area. $S=874f{t}^2$

Explanation of Solution

Given information : The following image is given. We can see here the radius $r=9ft$ and the height $h=20ft$ .

  

Formula used : The lateral area of the cone is $L=\pi rl$ and the surface area will be $S=\pi r^2+\pi rl$ . Where $r$ is the radius and $l$ is the slant height of the cone. Also, $l=\sqrt{h^2+r^2}$

Calculation : Calculate the slant height.

  $l=\sqrt{h^2+r^2}$

  $\begin{array}{l}l=\sqrt{{20}^2+9^2}\\ l=\sqrt{400+81}\\ l=\sqrt{481}\\ l=21.93ft\end{array}$

Now, find the lateral area.

  $L=\pi rl$

  $\begin{array}{l}L=\pi \times 9\times 21.93\\ L=619.7f{t}^2\end{array}$

And the surface area would be

  $\begin{array}{l}S=\pi r^2+\pi rl\\ S=(\pi \times 9^2)+(\pi \times 9\times 21.93)\\ S=254.3+619.7\\ S=874f{t}^2\end{array}$