Chapter 12.7, Problem 2CYU

To determine

To find: the lateral and surface area

Answer to Problem 2CYU

The surface area of the cone is $\text{163}\text{.28}{\text{in}}^2$ andthe lateral area of the cone is $113.04{\text{in}}^2$ .

Explanation of Solution

Given:

  

Formula used:

The lateral area L of a square pyramid is $L=\pi rl$ .

The surface area S of a square pyramid is S = L + B.

Calculation:

The given figure is a cone.

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

Find the lateral area of the cone.

Since radius is half the diameter of a circle, so radius of the circle is $\frac{8}{2}$ in. that is 4 in.

Substitute r= 4 and l = 9 in the lateral area formula to find the lateral area of the cone.

  $\begin{array}{c}L=\pi rl\\ =\pi \cdot 4\cdot 9\\ =36\pi \\ \approx 36\left(3.14\right)\left[Since\pi \approx 3.14\right]\\ =113.04\end{array}$

Therefore, the lateral area of the cone is $113.04{\text{in}}^2$ .

Find the surface area of the cone.

The area B of the square pyramid is $B={\left(side\right)}^2$

  $\begin{array}{c}B=\pi r^2\\ =\pi {\left(4\right)}^2\\ =16\pi \\ \approx 16\left(3.14\right)\left[Since\pi \approx 3.14\right]\\ =50.24\end{array}$

Substitute $B\approx 50.24$ and $L\approx 113.04$ in the surface area formula

  $\begin{array}{c}S=L+B\\ \approx 113.04+50.24\\ =163.28\end{array}$

Conclusion:

Therefore, the surface area of the cone is $\text{163}\text{.28}{\text{in}}^2$ andthe lateral area of the cone is $113.04{\text{in}}^2$ .