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