Chapter 12, Problem 17PT

To determine

To find the ratio of the volume of the large cylinder to the volume of the small cylinder.

Answer to Problem 17PT

  $3:1$

Explanation of Solution

Given:

Two similar cylinders:

Cylinder 1

Radius, $(r)=r$ centimeters

Height, $(h_1)=75$ centimeters

Cylinder 2

Radius, $(r)=r$ centimeters

Height, $(h_2)=25$ centimeters

Formula used:

Volume of the cylinder $=\pi r^{2}h$

where $r$ is the radius and $h$ is the height of the cylinder.

Calculation:

Volume of the cylinder 1:

Let $V$ be the volume of cylinder 1.

Volume $=\pi r^2{h}_1$

Now putting the values of $h_1$ ,

  $\Rightarrow \pi \times r^2\times 75$ cubic centimeters

Volume of the cylinder 2:

Let $V\text{'}$ be the volume of cylinder 2.

Volume $=\pi r^2{h}_2$

Now putting the values,

  $\Rightarrow \pi \times r^2\times 25$ cubic centimeters.

Now to find the ratio, divide volume of cylinder 1 by volume of cylinder 2.

  $\Rightarrow \frac{V}{V\text{'}}=\frac{\pi \times r^2\times 75}{\pi \times r^2\times 25}$

  $\Rightarrow \frac{V}{V\text{'}}=\frac{75}{25}$

  $\Rightarrow \frac{V}{V\text{'}}=\frac{3}{1}$

  $\Rightarrow V:V\text{'}=3:1$

Conclusion:

Hence, the ratio of volume of cylinder 1 to volume to cylinder 2 is $3:1$ .