Select the correct answer.

Question

The volume of a cylinder is 32.25 cubic inches. If a cone has the same height and radius as the cylinder, what is its volume?
A.
8.06 cu. in.
B.
10.75 cu. in.
C.
21.5 cu. in.
D.
32.25 cu. in.

Answer 1

The correct answer is B. 10.75 cu. in.

The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.

Since the cone has the same height and radius as the cylinder, its formula for the volume is 1/3πr^2h.

We know the volume of the cylinder is 32.25 cubic inches.

32.25 = πr^2h

Dividing both sides by πh gives us:

r^2 = 32.25/(πh)

Since the radius is the same for both the cylinder and the cone, we can use this equation to find the radius of the cone.

The formula for the volume of the cone is then:

V = 1/3πr^2h = 1/3π(32.25/(πh))h = 10.75 cu. in.

Therefore, the volume of the cone is 10.75 cubic inches, which is option B.