Chapter 12.3, Problem 16WE

To determine

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

Answer to Problem 16WE

The l =15units, h = 12units, total area = 678.24 sq. units, and lateral area = 423.9 sq. units

Explanation of Solution

Given information: Consider the given information,

Radius = 15units, Volume = $324\pi$ cu. units, $\pi \approx 3.14$

Formula used: Consider the given formula,

r = radius, h = height, l = length

  $l=\sqrt{{(r)}^2+{(h)}^2}$

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,

  $324\pi =\frac{1}{3}\pi \times {(9)}^2\times h$

  $h=\frac{324\times 3}{9\times 9}=12$ units

  $l=\sqrt{{(12)}^2+{(9)}^2}=\sqrt{225}=15$ units

Total area = $(3.14\times 9\times 15)+(3.14\times {(9)}^2)=678.24$ sq. units

Lateral area = $3.14\times 9\times 15=423.9$ sq. units