Chapter 12.8, Problem 32SR

To determine

To find: the lateral and surface area

Answer to Problem 32SR

The lateral area of the cone is a $188.4f{t}^2$ .

The surface area of the cone is $301.44f{t}^2$

Explanation of Solution

Given:

  

Formula used:

The lateral $L$ of a cone is calculated as

  $L=\pi rl$

The surface area $S$ of a cone is calculated as

  $S=L+B$

Calculation:

The objective is to find the lateral and surface area of the cone.

First find the lateral area of the cone.

Put $r=6$ and $l=10$ in the lateral area formula to find the lateral area of the cone.

Thus,

  $\begin{array}{l}L=\pi rl\\ =\pi \mathrm{.6.10}\\ =60\pi \\ \approx 60(3.14)[Since\pi \approx 3.14]\\ =188.4\end{array}$

Therefore, the lateral area of the cone is approximately $188.4f{t}^2$ .

Next find the surface area of the cone.

First find the area $B$ of the cone. The area $B$ of the base is given by

  $\begin{array}{l}B=\pi r^2\\ =\pi {\left(6\right)}^2\\ =36\pi \\ \approx 36(3.14)[Since\pi \approx 3.14]\\ =113.04\end{array}$

Put $B\approx 113.04$ and $L\approx 188.4$ in the surface area formula to find the surface area of the cone.

  $\begin{array}{l}S=L+B\\ \approx 188.4+113.04\\ =301.44\end{array}$

Therefore, the surface area of the cone is approximately $301.44f{t}^2$

Conclusion:

Therefore, the lateral area of the cone is $188.4f{t}^2$ and the surface area of the cone is $301.44f{t}^2$