Question

What is the ratio of the volumes of these two cylinders?Give your answer as a fraction in lowest terms.

Answer 1

Given:

The height and radius of the first cylinder is

`\begin{gathered} h1=7.5 \\ r1=3 \end{gathered}`

The height and radius of the second cylinder is

`\begin{gathered} h2=10 \\ r2=4 \end{gathered}`

Required:

To find the ratio of the volumes of these two cylinders.

Step-by-step explanation:

The formula for the volume of the cylinder is

`V=\pi r^2h`

Let V1 be the volume of the first cylinder and V2 be the volume of the second cylinder.

Now the ratio is

`\begin{gathered} =(V1)/(V2) \\ \\ =(\pi r1^2h1)/(\pi r2^2h2) \\ \\ =((3)^2*7.5)/((4)^2*10) \\ \\ =(9*7.5)/(16*10) \\ \\ =(67.5)/(160) \\ \\ =(13.5)/(32) \\ \\ =(1.7)/(4) \end{gathered}`

Final Answer:

The ratio of the volumes of these two cylinders is

`(1.7)/(4)`