The volume of a sphere is 72 m3 what is the volume of a cone if it’s radius is the same as the spheres and it’s height equal to the sphere diameter

Answer 1

We know that the volume of a sphere is given by the formula:

V = (4/3)πr^3

Given that the volume of the sphere is 72 m^3, we can rearrange the formula to solve for the radius:

r^3 = (3/4)V/π
r^3 = (3/4)(72)/(π)
r^3 = 216/π
r^3 ≈ 68.58
r ≈ 4.08 m

Now, let's find the diameter of the sphere:

d = 2r
d = 2(4.08)
d ≈ 8.17 m

The height of the cone is equal to the sphere's diameter, so the height of the cone is 8.17 m.

The volume of a cone is given by the formula:

V_cone = (1/3)πr^2h

Substituting the radius and height of the cone:

V_cone = (1/3)π(4.08)^2(8.17)
V_cone ≈ 56.02 m^3

Therefore, the volume of the cone is approximately 56.02 m^3.