Chapter 12.7, Problem 11PPS

To determine

To find: the lateral and surface area

Answer to Problem 11PPS

The surface area of the cone is a $175.84{\text{cm}}^2$ and the lateral area of the cone is $125.6{\text{cm}}^2$ .

Explanation of Solution

Given:

Consider the figure.

  

Formula used:

The lateral area L of a cone is given by the formula

  $L=\pi rl$

The surface area S of a cone is given by the formula

S = L + B

Calculation:

The given figure is a cone.

The objective is to find the lateral and surface area of the cone.

First find the lateral area of the cone.

Put r = 4 and l = 10 in the lateral area formula to find the lateral area of the cone.

Thus,

  $\begin{array}{c}L=\pi rl\\ =\pi \cdot 4\cdot 10\\ =40\pi \\ \approx 40\left(3.14\right)\left[Since\pi \approx 3.14\right]\\ =125.6\end{array}$

Therefore, the lateral area of the cone is approximately $125.6{\text{cm}}^2$ .

Next find the surface area of the cone.

First find the area B ofthe cone. The area B ofthe base is given by

  $\begin{array}{c}B=\pi r^2\\ =\pi {\left(44\right)}^2\\ =16\pi \\ \approx 16\left(3.14\right)\left[Since\pi \approx 3.14\right]\\ =50.24\end{array}$

Put $B\approx 50.24$ and $L\approx 125.6$ in the surface area formula to find the surface area of the cone.

  $\begin{array}{c}S=L+B\\ \approx 125.6+50.24\\ =175.84\end{array}$

Conclusion:

Therefore, the surface area of the cone is a $175.84{\text{cm}}^2$ and the lateral area of the cone is $125.6{\text{cm}}^2$ .