Chapter 12.7, Problem 17PPS

To determine

To find: the amount of material used to the make hats

Answer to Problem 17PPS

The amount of material required to make the hats is $1584in{.}_{}^2$

Explanation of Solution

Given:

Height is $18in.$ and circumference is $22in.$

Number of hats is 8

Formula Used:

The lateral area L of a cone is:

  $L=\pi rl$

Calculation:

The objective is to find the amount of material used to prepare the hats.

The amount of material used to prepare the hats. The amount of material prepare to one hat is the lateral area of the cone.

Find the lateral area of one cone. To find the lateral area find the radius of the circle.

The perimeter $p$ of a circle is $P=2\pi r$

  $P=2\pi r$

  $22=2\pi r$

  $\frac{22}{2}=\pi r$

  $11=\pi r$

  $\frac{11}{\pi }=r$

  $r=\frac{11}{\pi }$

Substitute $r=\frac{11}{\pi }$ and $l=18$ in $L=\pi rl$

Thus

  $L1=\pi rl$

  $=\cancel{\pi }.\frac{11}{\cancel{\pi }}\left(18\right)$

  $=11\left(18\right)$

  $=198$

Hence, the lateral area of a cone is $198in{.}_{}^2$

The lateral area $L$ of the eight cone is

  $L=8l1$

  $=8.198$

  $=1584$

Hence, the amount of material required to make the hats is $1584in{.}_{}^2$

Conclusion:

The amount of material required to make the hats is $1584in{.}_{}^2$