Chapter 12.3, Problem 12WE

To determine

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

Answer to Problem 12WE

The r =5.6units, lateral area = 105.504 sq. units, total area = 203.97 sq. units, and volume = 65.64 cu. units

Explanation of Solution

Given information: Consider the given information,

Height = 2units, Length = 6units, $\pi \approx 3.14$

Formula used: Consider the given formula,

r = radius, h = height, l = length

  $r=\sqrt{{(l)}^2-{(h)}^2}$

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,

  $r=\sqrt{{(6)}^2-{(2)}^2}=\sqrt{32}=5.6$ units

Lateral area = $3.14\times 5.6\times 6=105.504$ sq. units

Total area = $(3.14\times 5.6\times 6)+(3.14\times {(5.6)}^2)=203.97$ sq. units

Volume = $\frac{1}{3}\times 3.14\times {(5.6)}^2\times 2=65.64$ cu. units