The volume of a cone is 25/3 pi centimeters cubed what is the volume of a sphere if it's radius is the same as the cones and the height of the cone is equal to the Spheres diameter
Let's start by finding the radius of the cone. We know that the volume of the cone is given by the formula V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height.
Since the volume of the cone is (25/3)π cm³ and the height of the cone is equal to the sphere's diameter, let's denote the height of the cone as h and the radius as r. Therefore, we have the equation (25/3)π = (1/3)πr²h.
Since the height of the cone is equal to the diameter of the sphere, we can write h = 2r, where r is the radius of both the cone and the sphere.
Substituting this value of h into the equation, we get (25/3)π = (1/3)πr²(2r).
Simplifying, we have (25/3) = (1/3)2r³.
We can now solve for r:
(25/3) = (2/3)r³
25 = 2r³
12.5 = r³
r = ∛(12.5)
Now that we have found the radius of both the cone and the sphere, we can calculate the volume of the sphere. The formula for the volume of a sphere is given by V = (4/3)πr³.
Plugging in the radius we found, we get:
V = (4/3)π(∛(12.5))³
V = (4/3)π(2.5)
V = (10/3)π
Therefore, the volume of the sphere is (10/3)π cubic centimeters.