Question

The volume of a cone is 25/3 π cm3 . What is the volume of a sphere if its radius is the same as the cone’s and the height of the cone is equal to the sphere’s diameter?
a: 25/2 pi cm^3
b: 50/3 pi cm^3
c: 25/6 pi cm^3
d: 25 pi cm^3

Answer 1

b: 50/3 π cm^3

To find the volume of a sphere, we first need to calculate the radius and height of the cone.

Given that the volume of the cone is 25/3 π cm^3, we can use the formula for the volume of a cone: V = (1/3)πr^2h.

Now, we know that V = 25/3 π cm^3, and h = 2r (given that the height of the cone is equal to the diameter of the sphere).

Substitute these values into the volume formula:

25/3 π = (1/3)πr^2(2r)
25/3 π = (1/3)π(2r)^2
25 = (1/3)(4r^2)
25 = (4/3)r^2
r^2 = 25 * 3 / 4
r^2 = 18.75
r = √18.75
r ≈ 4.33 cm.

Now that we have the radius of the sphere, we can find its volume using the formula: V = (4/3)πr^3.

V = (4/3)π(4.33)^3
V ≈ 50/3 π cm^3

Therefore, the volume of the sphere is 50/3 π cm^3.