Chapter 12.3, Problem 15PPS

To determine

To find:

The lateral area and surface area of the cone.

Answer to Problem 15PPS

The lateral area of cone is $357.7{\text{ cm}}^2$ and the surface area is $470.84{\text{ cm}}^2$ .

Explanation of Solution

Given information:

A cone with diameter $12\text{ cm}$ and the height is $18\text{ cm}$ .

Calculation:

The lateral area of cone is $L=\pi rl$ , and the surface area of cone is $S=L+\pi r^2$ where $r$ is the radius of the base and $l$ be the slant height.

Radius of the base is $\frac{d}{2}$ .

So, the radius of the base of a cone is $6\text{ cm}$ .

The height is $18\text{ cm}$ .

Find the slant height.

  $\begin{array}{c}{l}^2=6^2+{18}^2\\ l=\sqrt{6^2+{18}^2}\\ =\sqrt{36+324}\\ =\sqrt{360}\\ =18.97\end{array}$

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

  $\begin{array}{c}L=\left(\pi \right)\left(6\right)\left(18.97\right)\\ =\left(\pi \right)113.82\\ =\left(\frac{22}{7}\right)113.82\\ =357.7\\ \approx 357.4\end{array}$

The surface area of cone is $S=L+\pi r^2$ .

  $\begin{array}{c}S=357.7+\pi {\left(6\right)}^2\\ =357.7+36\pi \\ =357.7+36\left(\frac{22}{7}\right)\\ =357.7+113.14\\ =470.84\end{array}$

Hence, the lateral area of cone is $357.7{\text{ cm}}^2$ and the surface area is $470.84{\text{ cm}}^2$ .