Chapter 12.3, Problem 16PPS

To determine

To find:

The lateral area and surface area of the cone.

Answer to Problem 16PPS

The lateral area of cone is $34.7{\text{ cm}}^2$ and the surface area is $43.776{\text{ cm}}^2$ .

Explanation of Solution

Given information:

A cone with diameter $\text{3}\text{.4 cm}$ and the slant height is $\text{6}\text{.5 cm}$ .

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 $\text{1}\text{.7 cm}$ .

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

  $\begin{array}{c}L=\left(\pi \right)\left(1.7\right)\left(6.5\right)\\ =\left(\pi \right)11.05\\ =\left(3.14\right)11.05\\ =34.69\\ \approx 34.7\end{array}$

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

  $\begin{array}{c}S=34.7+\pi {\left(1.7\right)}^2\\ =34.7+2.89\pi \\ =34.7+2.89\left(3.14\right)\\ =34.7+9.0746\\ =43.776\end{array}$

Hence, the lateral area of cone is $34.7{\text{ cm}}^2$ and the surface area is $43.776{\text{ cm}}^2$ .