Chapter 12.3, Problem 18PPS

To determine

To find:

The lateral area of the mountain.

Answer to Problem 18PPS

The lateral area of cone is $8.54$ square kilometers.

Explanation of Solution

Given information:

A cone with radius of $1.6$ kilometers and the height $0.5$ kilometers.

Calculation:

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

Find the slant height of the mountain cone.

Apply this formula to find the radius.

  $\begin{array}{l}{l}^2=r^2+h^2\\ l=\sqrt{r^2+h^2}\end{array}$

Substitute $r=1.6$ and $h=0.5$ in the above formula.

  $\begin{array}{c}l=\sqrt{{\left(1.6\right)}^2+{0.6}^2}\\ =\sqrt{2.56+0.36}\\ =\sqrt{2.92}\\ =1.70\end{array}$

So, the slant height of a cone is $1.70$ kilometers.

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

  $\begin{array}{c}L=\left(\pi \right)\left(1.6\right)\left(1.70\right)\\ =\left(\pi \right)2.72\\ =\left(3.14\right)2.72\\ =8.54\end{array}$

Hence, the lateral area of cone is $8.54$ square kilometers.