Chapter 12.3, Problem 4CYP

To determine

To find:

The lateral area of the cone.

Answer to Problem 4CYP

The lateral area of cone is $\text{22}\text{.14}$ square inches.

Explanation of Solution

Given information:

A waffle cone is $5\frac{1}{2}$ inches tall and the diameter of the base is $2\frac{1}{2}$ inches.

Calculation:

The lateral area of cone is $L=\pi rl$ , where $r$ is the radius of the base and $l$ be the slant height.

Diameter of the base is $2\frac{1}{2}=\frac{5}{2}$ inches.

  $\begin{array}{c}r=\frac{d}{2}\\ =\frac{\frac{5}{2}}{2}\\ =\frac{5}{4}\end{array}$

So, the radius of the base is $\frac{5}{4}$ inches.

Now, find the slant height $l$ .

  

  $\begin{array}{c}{l}^2={\left(\frac{11}{2}\right)}^2+{\left(\frac{5}{4}\right)}^2\\ l=\sqrt{{\left(\frac{11}{2}\right)}^2+{\left(\frac{5}{4}\right)}^2}\\ =\sqrt{\frac{121}{4}+\frac{25}{16}}\\ =\sqrt{\frac{484+25}{16}}\\ =\sqrt{\frac{509}{16}}\\ =\frac{22.56}{4}\end{array}$

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

  $\begin{array}{c}L=\left(3.14\right)\left(\frac{5}{4}\right)\left(\frac{22.56}{4}\right)\\ =\left(3.14\right)\left(\frac{112.8}{16}\right)\\ =\frac{354.192}{16}\\ =22.137\\ \approx 22.14\end{array}$

Hence, the lateral area of cone is $\text{22}\text{.14}$ square inches.