Chapter 12.3, Problem 14PPS

To determine

To find:

The lateral area and surface area of the cone.

Answer to Problem 14PPS

The lateral area of cone is $138.2$ square inches and the surface area is $188.5$ square inches.

Explanation of Solution

Given information:

A cone with radius $4$ inches and the slant height be $11$ inches.

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 $r=4$ inches.

The slant height is $l=11$ inches.

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

  $\begin{array}{c}L=\left(\pi \right)\left(4\right)\left(11\right)\\ =\left(\pi \right)44\\ =\left(3.14\right)44\\ =138.16\\ \approx 138.2\end{array}$

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

  $\begin{array}{c}S=138.2+\pi {\left(4\right)}^2\\ =138.2+16\pi \\ =138.2+16\left(\frac{22}{7}\right)\\ =138.2+50.28\\ =188.48\\ \approx 188.5\end{array}$

Hence, the lateral area of cone is $138.2$ square inches and the surface area is $188.5$ square inches.