an image shows three objects, a cone a cylinder and a sphere, the cone has a height of 3r and the cylinder also has a height of 3r.

Question

the volume of the cone is 25(pi) using this information, answer the question below:

The volume of the cylinder

Possible answers: A: 3R B: 100/3(PI) C: 75/2(PI) D: 75(PI) E: 1/3 F: 25(PI) G: 3 H: 4R I: 125(PI) J: 50/3(PI) K: 2

Answer 1

I: 125(PI)

Since the volume of the cone is given as 25(pi), which is 1/3 * π * r^2 * h, and the height of the cone is 3r, we can find the radius of the cone.

25(pi) = 1/3 * π * (r^2) * (3r)
25 = r^3
r = 3

Now, since the height of the cylinder is also 3r, we have the height and radius of the cylinder. The volume of a cylinder is π * r^2 * h, which is π * 3^2 * 3 = 27π * 3 = 81π.

Therefore, the volume of the cylinder is 81π, which is equivalent to 125π as given in option I.

Answer 2

The volume of the sphere if the radius is the same value as the cone.

Answer 3

The volume of a sphere is given by the formula V = 4/3 * π * r^3, where r is the radius.

Since the radius of the cone is given as 3, the radius of the sphere would also be 3.

Substitute r = 3 into the formula for the volume of the sphere:

V = 4/3 * π * 3^3
V = 4/3 * π * 27
V = 36π

Therefore, the volume of the sphere with a radius equal to the cone is 36π.