The volume of a cone is 25/3 pi cm³ what is the volume of a sphere if it's radius is the same as the cones and the height of the cones is equal to the spheres diameter
Let's first find the radius and height of the cone.
Given that the volume of the cone is (25/3)π cm³, we can use the formula for the volume of a cone which is (1/3)πr²h, where r is the radius and h is the height.
Since the volume of the cone is known and equal to (25/3)π cm³, we have:
(1/3)πr²h = (25/3)π
Dividing both sides by (1/3)π, we get:
r²h = 25
Now, let's move on to the sphere. We are given that the radius of the sphere is the same as the radius of the cone. Let's denote the radius as r as well.
The volume of a sphere can be calculated using the formula (4/3)πr³.
Since the radius of the sphere is the same as the radius of the cone, we have r = r, which means r² = r³.
Also, we are given that the height of the cone is equal to the diameter of the sphere, which means the diameter of the sphere is 2r. From this, we can deduce that the radius of the sphere is r.
Therefore, the volume of the sphere will be (4/3)πr³. Since r² = r³, we can rewrite this as (4/3)π(r²)h.
Substituting r²h = 25, which we found for the cone:
(4/3)π(r²)h = (4/3)π(25)
The (4/3)π cancels out on both sides, leaving us:
r²h = 100
So, the volume of the sphere is 100 cm³.