The volume of a sphere is 72 m^3 . What is the volume of a cone if its radius is the same as the sphere’s and its height is equal to the sphere’s diameter

Answer 1

First, let's find the radius of the sphere:
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere.

So, 72 = (4/3)πr^3
72 = 4πr^3 / 3
72 * 3 = 4πr^3
216 = 4πr^3
r^3 = 216 / (4π)
r^3 = 54 / π
r ≈ (54 / π)^(1/3)
r ≈ 3.63 m

Now, let's find the volume of the cone:
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius of the cone and h is the height of the cone.

Since the radius of the cone is the same as the sphere's radius, r = 3.63 m, and the height of the cone is equal to the sphere's diameter, which is twice the radius, h = 2 * 3.63 = 7.26 m.

Therefore, the volume of the cone is:
V = (1/3)π(3.63)^2 * 7.26
V = (1/3)π * 13.1469 * 7.26
V = (1/3) * 95.427327 * π
V ≈ 100.06 m^3

So, the volume of the cone is approximately 100.06 m^3.