Chapter SH, Problem 12.7.2EP

To determine

To find: the lateral area and surface area

Answer to Problem 12.7.2EP

The lateral area and surface area are $377c{m}^2,578.1c{m}^2$ .

Explanation of Solution

Given:

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.

Perimeter of the base is

  $\begin{array}{l}P=2\pi r\\ P=2\pi \times 8\to P=16\pi \end{array}$

Slant height is $I=15cm$

Here base is a circle.

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

  $\begin{array}{l}B=\pi r^2\\ =\pi {\left(8\right)}^2\\ =64\pi \end{array}$

Lateral area is

  $\begin{array}{l}L=\frac{1}{2}PI\\ =\frac{1}{2}\times 16\times 15\\ =120\pi \\ \approx 377\end{array}$

Surface area is

  $\begin{array}{l}S=L+B\\ =120\pi +64\pi \\ =184\pi \\ \approx 578.1\end{array}$

Hence, the lateral area and surface area are $377c{m}^2,578.1c{m}^2$ .

Conclusion:

Hence, the lateral area and surface area are $377c{m}^2,578.1c{m}^2$ .