Chapter 12.5, Problem 11PSB

To determine

To calculate: The cone volume by removing the smaller cone from the larger cone.

Answer to Problem 11PSB

The cone volume is $72\pi$ .

Explanation of Solution

Given information:

Radius of both cones = 6,

Height of smaller cone = 4,

Height of larger cone = 10.

Formula used:

Volume of cone $=\frac{1}{3}\times B\times h$

B = Base area of cone and h = height of cone

Area of a circle: $A=\pi r^2$

r = radius of circle

Calculation:

  

Volume of smaller cone:

  $B=\pi r^2=\pi {\left(6\right)}^2=36\pi$

Height of smaller cone h = 4

  $\begin{array}{l}{V}_{Smallercone}=\frac{1}{3}\times B\times h\\ V_{Smallercone}=\frac{1}{3}\times 36\pi \times 4\\ V_{Smallercone}=48\pi \end{array}$

Volume of larger cone:

  $B=\pi r^2=\pi {\left(6\right)}^2=36\pi$

Height of larger cone h = 10

  $\begin{array}{l}{V}_{Smallercone}=\frac{1}{3}\times B\times h\\ V_{Smallercone}=\frac{1}{3}\times 36\pi \times 10\\ V_{Smallercone}=120\pi \end{array}$

Cone Volume = Volume of larger cone - Volume of smaller cone

Cone Volume $=120\pi -48\pi$

Cone Volume $=72\pi$