Chapter 12, Problem 12CR

To determine

To calculate:The change in the volume of the cylinder

Answer to Problem 12CR

The volume of cylinder does not change.

Explanation of Solution

Given information:

Two cylinders are given.

Calculation:

Let $C$ and $C\text{'}$ are two cylinder.

  

From the above figure

• $r$ is the radius of cylinder, $C$ .
• $h$ isthe height of cylinder, $C$ .
• $V$ is volume of cylinder, $C$ .
• $r\text{'}$ is the radius of cylinder, $C\text{'}$ .
• $h\text{'}$ is the height of cylinder, $C\text{'}$ .
• $V\text{'}$ is volume of cylinder, $C\text{'}$ .

Write the expression to calculate the volume of the cylinder.

  $\begin{array}{c}V=\pi \times r^2\times h\\ =\pi r^{2}h\end{array}$

Calculate the radius $r\text{'}$ of cylinder $C\text{'}$ .

  $r\text{'}=2r$

Calculate the height $h\text{'}$ of cylinder $C\text{'}$ .

  $h\text{'}=\frac{h}{2}$

Write the expression to calculate the volume $V\text{'}$ of the cylinder $C\text{'}$ .

  $\begin{array}{c}V\text{'}=\pi \times r{\text{'}}^2\times h\text{'}\\ =\pi \times 4r^2\times \frac{h}{2}\\ =2\pi r^{2}h\end{array}$

Determine the change in the volume.

  $\begin{array}{c}V\text{'}\text{'}=V\text{'}-V\\ =2\pi r^{2}h-\pi r^{2}h\\ =\pi r^{2}h\end{array}$

From the above, it is clear that the volume of the cylinder does not change.

Therefore, thevolume of the cylinder does not change.