Chapter 4.5, Problem 64HP

To determine

To find: The lateral area of the cone.

Answer to Problem 64HP

The value of lateral area is $90.55{\text{in}}^2$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Consider the slant height of the cone is,

  $\begin{array}{l}{l}^2={\left(6\text{in}\right)}^2+{\left(4\text{in}\right)}^2\\ l^2=36{\text{in}}^2+16{\text{in}}^2\\ l=\sqrt{52{\text{in}}^2}\\ l=7.21\text{in}\end{array}$

Consider the formula for the lateral area of the cone is,

  $A=\pi rl$

Then,

  $\begin{array}{c}A=\left(3.14\right)\left(4\right)\left(7.21\right)\\ =90.55{\text{in}}^2\end{array}$