Chapter 12.10, Problem 2GP

To determine

To find:Thelateral surface area and surface area of the cone.

Answer to Problem 2GP

Thelateral surface area and surface area of the cone is $113.1{\text{in}}^2$ and $163.4{\text{in}}^2$ , respectively.

Explanation of Solution

Given information:

The slant height of the cone is 9 inches and diameter is 8 inches.

Calculation:

Calculate the radius of the cone.

  $\begin{array}{c}r=\frac{8}{2}\\ =4\text{inches}\end{array}$

Write the expression to calculate the lateral surface area.

  $L=\pi rl$

Where,

• $r$ is the radius.
• $l$ is the slant height.

Substitute the values in the above.

  $\begin{array}{c}L=\pi \cdot 4\cdot 9\\ =36\pi {\text{in}}^2\\ =113.1{\text{in}}^2\end{array}$

Write the expression to calculate the total surface area.

  $S=\text{Lateral}\text{surface}\text{area}+\text{Base}\text{area}$

Substitute the values in the above expression.

  $\begin{array}{c}S=36\pi {\text{in}}^2+\pi {\left(4\right)}^2{\text{in}}^2\\ =36\pi {\text{in}}^2+16\pi {\text{in}}^2\\ =52\pi {\text{in}}^2\\ =163.4{\text{in}}^2\end{array}$

Conclusion:

Therefore, the lateral surface area and surface area of the cone is $113.1{\text{in}}^2$ and $163.4{\text{in}}^2$ , respectively.