Question

A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.

Use pi = 3.14.

What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.

Answer 1

We can say that volume of cylinder (452.16) is greater than volume of cone (301.44).

Explanation:

Diameter of cylinder = 8 inches

Diameter of cone = 8 inches

Height of cylinder = 9 inches

Height of cone = 18 inches

We need to find the relationship between the volume of this cylinder and this cone.

First we will find volume of the cylinder

The formula used is:
`Volume=\pi r^2h`

We have

Diameter of cylinder = 8 inches

Radius = d/2 = 8/2 = 4 inches.

Height of cylinder = 9 inches

Putting values and finding volume

`Volume=\pi r^2h\\Volume=3.14* (4)^2 * 9\\Volume=452.16`

So, Volume of cylinder = 452.16 inches³

Now, we will find volume of the cone

The formula used is:
`Volume=\pi r^2(h)/(3)`

We have

Diameter of cone = 8 inches

Radius = d/2 = 8/2 = 4 inches.

Height of cone = 9 inches

Putting values and finding volume

`Volume=\pi r^2(h)/(3)\\Volume=3.14 * (4)^2 * (18)/(3)\\Volume=3.14 * (4)^2 * 6\\Volume=301.44`

So, Volume of cone = 301.44 inches³

Now, comparing volume of both cylinder and cone.

Volume of cylinder = 452.16 inches³

Volume of cone = 301.44 inches³

We can say that volume of cylinder (452.16) is greater than volume of cone (301.44).