Chapter SH, Problem 12.7.6EP

To determine

To find: the lateral area and surface area of cone

Answer to Problem 12.7.6EP

The lateral area and surface area are $88i{n}^2,138.2i{n}^2$ .

Explanation of Solution

Given:

Radius of the cone is $4in$ .

Slant height is $7in$ .

Formula used:

Lateral area of the pyramid is $L=\frac{1}{2}PI$

Total surface area of the prism is $S=L+B$

Lateral area of the pyramid is

  $L=\frac{1}{2}PI$

Here $P$ is the base perimeter and $I$ is the slant height.

Total surface area of the prism is

  $S=L+B$

Here $B$ is the area of base.

Here base is a circle.

Perimeter of the base is

  $\begin{array}{l}P=2\pi r\\ P=2\pi \times 4\to P=8\pi \end{array}$

Slant height is $I=7in$ .

Area of the base is $\pi r^2$ .

  $\begin{array}{l}B=\pi r^2\\ =\pi {\left(4\right)}^2\\ =16\pi \end{array}$

Lateral area is

  $\begin{array}{l}L=\frac{1}{2}PI\\ =\frac{1}{2}\times 8\pi \times 7\\ =28\pi \\ \approx 88\end{array}$

Surface area is

  $\begin{array}{l}S=L+B\\ =28\pi +16\pi \\ =44\pi \\ \approx 138.2\end{array}$

Hence, the lateral area and surface area are $88i{n}^2,138.2i{n}^2$ .

Conclusion:

Hence, the lateral area and surface area are $88i{n}^2,138.2i{n}^2$ .