Chapter 12.7, Problem 13PPS

To determine

To find: the lateral and surface area

Answer to Problem 13PPS

The surface area of the cone is $628{\text{ft}}^2$ .

The lateral area of the cone is $427.04{\text{ft}}^2$

Explanation of Solution

Given:

  

Formula used:

The lateral area L of a cone is $L=\pi rl$

The surface area S of a cone is S = L + B.

Calculation:

Find the lateral area of the cone as follows:

Substitute r = 8 and l = 17 in $L=\pi rl$ .

Thus,

  $\begin{array}{c}L=\pi rl\\ =\pi \cdot 8\cdot 17\\ =136\pi \\ \approx 136\left(3.14\right)As\pi \approx 3.14\\ =427.04\end{array}$

Hence, the lateral area of the cone is approximately $427.04{\text{ft}}^2$

Find the surface area of the cone as follows:

The area B of the base is,

  $\begin{array}{c}B=\pi r^2\\ =\pi {\left(8\right)}^2\\ =64\pi \\ \approx 64\left(3.14\right)As\pi \approx 3.14\\ =200.96\end{array}$

Substitute $B\approx 200.96$ and $L\approx 427.04$ in S = L + B

  $\begin{array}{c}S=L+B\\ \approx 427.04+200.96\\ =628\end{array}$

Conclusion:

Hence, the surface area of the cone is $628{\text{ft}}^2$ and the lateral area of the cone is $427.04{\text{ft}}^2$