Question

Cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 5 inches. The height of the cone is 15 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

Answer:

$V_{cylinder}=251.2\ in^3,$

$V_{cone}=251.2\ in^3,$

$V_{cylinder}=V_{cone}.$

Step-by-step explanation:

The volume of the cylinder is

$V_{cylinder}=\pi r^2 h,$

where r is the radius of a base circle and h is the cylinder's height.

If cylinder has diameter of 8 inches, then its radius is 4 inches. The height of the cylinder is 5 inches. Thus, the volume of the cylinder is

$V_{cylinder}=3.14\cdot 4^2\cdot 5=251.2\ in^3.$

The volume of the cone is

$V_{cone}=\dfrac{1}{3}\pi r^2 h,$

where r is the radius of a base circle and h is the cone's height.

If cone has diameter of 8 inches, then its radius is 4 inches. The height of the cone is 15 inches. Thus, the volume of the cone is

$V_{cylinder}=\dfrac{1}{3}\cdot 3.14\cdot 4^2\cdot 15=251.2\ in^3.$

As you can see the cylinder and the cone have the same volume.