Chapter 12.7, Problem 20PPS

To determine

To find: the lateral and total surface area

Answer to Problem 20PPS

The surface area of the cone is approximately $\text{1648}{\text{.5 in}}^2$ .

the lateral area of the cone is approximately ${\text{942 in}}^2$ .

Explanation of Solution

Given:

  

Formula used:

The lateral area L ofaconeis $L=\pi rl$ .

The surface area S ofaconeis S=L+B

Calculation:

Consider the figure as shown below:

  

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

Find the lateral area of the cone as follows:

  $\begin{array}{l}L=\pi rl\\ =\pi \cdot 15\cdot 20\\ =300\pi \\ \approx 300\left(3.14\right)\text{ As }\pi \approx \text{3}\text{.14}\\ \text{=942}\end{array}$

Hence, the lateral area of the cone is approximately ${\text{942 in}}^2$ .

Find the surface area of the cone as follows:

The area B ofthe base is,

  $\begin{array}{l}B=\pi r^2\\ =\pi {\left(5\right)}^2\\ =225\pi \\ \approx 225\left(3.14\right)\text{ As }\pi \approx \text{3}\text{.14}\\ \text{=706}\text{.5}\end{array}$

Substitute $B\approx 706.5$ and $L\approx 942$ in $S=L+B$ .

  $\begin{array}{l}S=L+B\\ \approx 942+706.5\\ =1648.5\end{array}$

Hence, the surface area of the cone is approximately $\text{1648}{\text{.5 in}}^2$ .

Conclusion:

Hence, the surface area of the cone is approximately $\text{1648}{\text{.5 in}}^2$ andthe lateral area of the cone is approximately ${\text{942 in}}^2$ .