Chapter 12.3, Problem 13WE

To determine

To calculate: The lateral area, total area, and volume of the cone.

Answer to Problem 13WE

The r =12units, h = 9units, total area = 1017.36 sq. units, and volume = 1356.48 cu. units

Explanation of Solution

Given information: Consider the given information,

Length = 15units, Lateral area = $180\pi$ sq. units, $\pi \approx 3.14$

Formula used: Consider the given formula,

r = radius, h = height, l = length

  $r=\sqrt{{(l)}^2-{(h)}^2}$

  $h=\sqrt{{(l)}^2-{(r)}^2}$

Lateral area = $\pi rl$

Total area = $\pi rl+\pi r^2$

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

Calculation : Consider the given information the formula is,

  $180\pi =\pi \times r\times 15$

  $r=12$ units

  $h=\sqrt{{(15)}^2-{(12)}^2}=\sqrt{81}=9$ units

Total area = $(3.14\times 12\times 15)+(3.14\times {(12)}^2)=1017.36$ sq. units

Volume = $\frac{1}{3}\times 3.14\times {(12)}^2\times 9=1356.48$ cu. units