Chapter 12.3, Problem 14WE

To determine

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

Answer to Problem 14WE

The l =29units, h = 20units, total area = 3297 sq. units, and volume = 9231.6 cu. units

Explanation of Solution

Given information: Consider the given information,

Length = 15units, Lateral area = $609\pi$ sq. units $609\pi$ , $\pi \approx 3.14$

Formula used: Consider the given formula,

r = radius, h = height, l = length

  $h=\sqrt{{(l)}^2-{(r)}^2}$

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,

  $609\pi =\pi \times 21\times l$

  $l=29$ units

  $h=\sqrt{{(29)}^2-{(12)}^2}=\sqrt{400}=20$ units

Total area = $(3.14\times 21\times 29)+(3.14\times {(21)}^2)=3297$ sq. units

Volume = $\frac{1}{3}\times 3.14\times {(21)}^2\times 20=9231.6$ cu. units