Chapter 12.3, Problem 22PPS

To determine

To find:

Which is more Tepee $A$ or Tepee $B$ .

Answer to Problem 22PPS

  $219.9{\text{ ft}}^2$ more canvas is used to make Tepee $B$ than Tepee $A$ .

Explanation of Solution

Given information:

The dimensions of the two canvas tepees are shown in the table:

Tepee	Diameter(ft)	Height(ft)
$A$	$14$	$6$
$B$	$20$	$9$

Calculation:

For tepee $A$ :

First find the radius and slant height.

  $\begin{array}{c}r=\frac{d}{2}\\ =\frac{14}{2}\\ =7\end{array}$

So, the radius is $7\text{ ft}$ .

Now, find the slant height using this formula:

  $\begin{array}{c}l=\sqrt{r^2+h^2}\\ =\sqrt{7^2+6^2}\\ =\sqrt{85}\end{array}$

So, the slant height is $\sqrt{85}\text{ ft}$ .

Lateral area of canvas $A$ is $\pi rl$ .

  $\begin{array}{c}L=\pi \left(7\right)\left(\sqrt{85}\right)\\ =\pi 64.47\\ \approx 202.75\end{array}$

So, the lateral area of canvas $A$ is $\text{202}{\text{.75 ft}}^2$ .

For tepee $B$ :

First find the radius and slant height.

  $\begin{array}{c}r=\frac{d}{2}\\ =\frac{20}{2}\\ =10\end{array}$

So, the radius is $\text{10 ft}$ .

Now, find the slant height using this formula:

  $\begin{array}{c}l=\sqrt{r^2+h^2}\\ =\sqrt{{10}^2+9^2}\\ =\sqrt{181}\end{array}$

So, the slant height is $\sqrt{181}\text{ ft}$ .

Lateral area of canvas $A$ is $\pi rl$ .

  $\begin{array}{c}L=\pi \left(10\right)\left(\sqrt{181}\right)\\ =\pi \left(10\right)\left(13.45\right)\\ =\pi 134.5\\ \approx 422.66\end{array}$

So, the lateral area of canvas $B$ is $422.66{\text{ ft}}^2$ .

Then find the difference between the value of canvas $B$ and canvas $A$ .

  $422.66-202.75=219.9{\text{ ft}}^2$ .

  $219.9{\text{ ft}}^2$ more canvas is used to make Tepee $B$ than Tepee $A$ .