The volume of a cone is 25/3 π cm^3. What is the volume of a sphere if its radius is the same as the cones and the height of the cone is equal to the spheres diameter?
a 50/3 π cm^3
b 25 π cm^3
c 25/6 π cm^3
d 25/2 π cm^3
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.
In this case, let's let the radius of the cone be r and the height be 2r (since the height of the cone is equal to the sphere's diameter).
We are given that the volume of the cone is (25/3)π cm^3:
(1/3)πr^2(2r) = (25/3)π
2r^3 = 25/3
r^3 = 25/6
To find the volume of the sphere, we can use the formula V = (4/3)πr^3, where r is the radius.
Substituting r^3 = 25/6, we get:
V = (4/3)π(25/6)
V = (100/18)π
V = (50/9)π
Therefore, the volume of the sphere is 50/9π cm^3.
The correct answer is not provided in the given options.