Chapter 12.3, Problem 38WE

To determine

To calculate: The volume of the cone

Answer to Problem 38WE

The volume of the cone is $23.68$ cubic inches

Explanation of Solution

Given information: Consider the given information,

Radius = 6in.

Angle of the cut-out sector = ${120}^{\circ }$

Formula used: Consider the given formula,

r = radius, h = height

Sector = total circumference $\times \frac{120}{360}$

Volume = $\frac{1}{3}\pi r^{2}h$

Calculation : Consider the given information the formula is,

Sector = $2\pi \times 6\times \frac{1}{3}$ = $4\pi$

Radius of cone is,

  $4\pi =2\pi r_2$ ( $r_2$ =second radius)

  $r_2=2$ in.

  $height=\sqrt{{(6)}^2-{(2)}^2}$

  $=\sqrt{36-4}$

  $=\sqrt{32}$

  $=4\sqrt{2}$ in.

Therefore, volume of the cone = $=\frac{1}{3}\pi \times 4\sqrt{2}\times {(2)}^2$

  $=23.68$ cubic inches