Chapter SH, Problem 12.7.4EP

To determine

To find: the lateral area and surface area

Answer to Problem 12.7.4EP

The lateral area and surface area are $61.4m^2,75.2m^2$ .

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.

Here base is a circle.

Radius is $r=\frac{1}{2}\left(4.2\right)\to r=2.1$

Perimeter of the base is

  $\begin{array}{l}P=2\pi r\\ P=2\pi \times 2.1\\ P=4.2\pi \end{array}$

Slant height is $I=9.3m$

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

  $\begin{array}{l}B=\pi r^2\\ =\pi {\left(2.1\right)}^2\\ =4.41\pi \end{array}$

Lateral area is

  $\begin{array}{l}L=\frac{1}{2}PI\\ =\frac{1}{2}\times 4.2\pi \times 9.3\\ =19.53\pi \approx 61.4\end{array}$

Surface area is

  $\begin{array}{l}S=L+B\\ =19.53\pi +4.41\pi \\ =23.94\pi \\ \approx 75.2\end{array}$

Hence, the lateral area and surface area are $61.4m^2,75.2m^2$ .

Conclusion:

Hence, the lateral area and surface area are $61.4m^2,75.2m^2$ .