Chapter 12.4, Problem 22PSC

To determine

To calculate: The volume of the solid.

Answer to Problem 22PSC

The volume of solid is $282.74i{n}^3$ .

Explanation of Solution

Given information:

Diameter of circle d = 6 in,

Height h₁ = 8 in,

Height h₂ =12-8 = 4 in.

Formula used:

Volume of cylinder $=B\times h$

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

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

r = radius of circle

Calculation:

  

d = 12

  $r=\frac{d}{2}=\frac{12}{2}=6$

Separate the cylinder into a cylinder and a half cylinder.

The height of the top cylinder is 12 − 8 = 4

  $\begin{array}{l}{V}_{Cylinder1}=B\times h_1\\ V_{Cylinder1}=\pi r^2\times h_1\\ V_{Cylinder1}=\pi {\left(3\right)}^2\times 8\\ V_{Cylinder1}=9\pi \times 8\\ V_{Cylinder1}=72\pi \\ V_{Cylinder1}=226.19i{n}^3\end{array}$

  $\begin{array}{l}{V}_{Cylinder2}=\frac{1}{2}B\times h_2\\ V_{Cylinder2}=\frac{1}{2}\pi r^2\times h_2\\ V_{Cylinder2}=\frac{1}{2}\pi {\left(3\right)}^2\times 4\\ V_{Cylinder2}=9\pi \times 2\\ V_{Cylinder2}=18\pi \\ V_{Cylinder2}=56.54i{n}^3\end{array}$

Total Volume $=V_{Cylinder1}+V_{Cylinder2}$

Total Volume $=226.19+56.54$

Total Volume $=282.74i{n}^3$