Chapter 12.3, Problem 15WE

To determine

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

Answer to Problem 15WE

The l =25 units, h = 20 units, total area = 1884 sq. units, and lateral area = 1177.5sq. units

Explanation of Solution

Given information: Consider the given information,

Radius = 15 units, Volume = $609\pi$ 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,

  $600\pi =\frac{1}{3}\pi \times {(15)}^2\times h$

  $h=\frac{600\times 3}{15\times 15}=20$ units

  $l=\sqrt{{(20)}^2+{(15)}^2}=\sqrt{625}=25$ units

Total area = $(3.14\times 15\times 25)+(3.14\times {(15)}^2)=1884$ sq. units

Lateral area = $3.14\times 15\times 25=1177.5$ sq. units