Michael has two different shaped containers. The dimensions of each container are shown in the drawing.

Cylinder
Radius: 3 in.
Height: 8 in.
Cone
Radius: 2.5 in.
Height: 9 in.

Which statement about the volumes of the cone and the cylinder is true?

A The volume of the cylinder is 167.29 cubic inches less than the volume of the cone.

B The volume of the cylinder is 48 89 cubic inches less than the volume of the cone.

C The volume of the cone is 48.89 cubic inches greater than the volume of the cylinder.

D The volume of the cone is 167.29 cubic inches less than the volume of the cylinder.

1 answer

To calculate the volume of a cylinder, you use the formula V = πr^2h, where r is the radius and h is the height.
For the cylinder:
V = π(3^2)(8) = 72π ≈ 226.19 cubic inches

To calculate the volume of a cone, you use the formula V = (1/3)πr^2h.
For the cone:
V = (1/3)π(2.5^2)(9) = 18.75π ≈ 58.89 cubic inches

Then, calculating the difference in volume:
58.89 - 226.19 ≈ -167.30

Therefore, the statement A "The volume of the cylinder is 167.29 cubic inches less than the volume of the cone." is true.