Chapter 12.3, Problem 4CE

(a)

To determine

To find: The volume of cylinders $\text{I,}\text{II}$ , and $\text{III}$ .

Answer to Problem 4CE

The volume of cylinders $\text{I,}\text{II}$ , and $\text{III}$ is $36\pi ,72\pi ,$ and $144\pi$ respectively.

Explanation of Solution

Given information:

The given figure is shown below.

  

Figure (1)

Calculation:

The volume of a cylinder is given by formula.

  $\pi r^{2}h$

Here, $r$ is the radius and $h$ is the height.

The values for the cylinder $\text{I}$ .

  $\begin{array}{l}r=3\\ h=4\end{array}$

Calculate the volume for the cylinder $\text{I}$ .

  $\begin{array}{c}\pi r^{2}h=\pi \times 3^2\times 4\\ =36\pi \end{array}$

The values for the cylinder $\text{II}$ .

  $\begin{array}{l}r=3\\ h=8\end{array}$

Calculate the volume for the cylinder $\text{II}$ .

  $\begin{array}{c}\pi r^{2}h=\pi \times 3^2\times 8\\ =72\pi \end{array}$

The values for the cylinder $\text{III}$ .

  $\begin{array}{l}r=6\\ h=4\end{array}$

Calculate the volume for the cylinder $\text{III}$ .

  $\begin{array}{c}\pi r^{2}h=\pi \times 6^2\times 4\\ =144\pi \end{array}$

Therefore, the volume of cylinders $\text{I,}\text{II}$ , and $\text{III}$ is $36\pi ,72\pi ,$ and $144\pi$ respectively.

(b)

To determine

To find: Whether the volume of $\text{II}$ is twice the volume of $\text{I}$ .

Answer to Problem 4CE

The yes, the volume of $\text{II}$ is twice the volume of $\text{I}$ .

Explanation of Solution

Given information:

The height of $\text{II}$ is twice the height of $\text{I}$ .

Calculation:

Calculate the volume for the cylinder $\text{II}$ .

  $\begin{array}{c}\pi r^{2}h=\pi \times 3^2\times 8\\ =72\pi \\ =2\left(36\pi \right)\\ =2\left(\text{Volume}\text{of}\text{cylinder}\text{I}\right)\end{array}$

Therefore, yes, the volume of $\text{II}$ is twice the volume of $\text{I}$ .

(c)

To determine

To find: Whether the volume of $\text{III}$ is twice the volume of $\text{I}$ .

Answer to Problem 4CE

The No, the volume of $\text{III}$ is not twice the volume of $\text{I}$ .

Explanation of Solution

Given information:

The height of $\text{II}$ is twice the height of $\text{I}$ .

Calculation:

Calculate the volume for the cylinder $\text{III}$ .

  $\begin{array}{c}\pi r^{2}h=\pi \times 6^2\times 4\\ =144\pi \\ =2\left(72\pi \right)\end{array}$

Therefore, the volume of $\text{III}$ is not twice the volume of $\text{I}$ .