Question

The volume of a sphere is 72 m3

. 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?(1 point)
m3

Answer 1

[AI-generated answer — Bot GPT 3.5]

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 solve for the radius (r) as follows:
72 = (4/3)πr^3
Dividing both sides by (4/3)π:
r^3 = 72 / (4/3)π
Simplifying:
r^3 = 54 / π
Taking the cube root of both sides:
r = (54 / π)^(1/3)

The height of the cone is equal to the sphere's diameter, which is 2r:
h = 2r = 2 (54 / π)^(1/3)

The volume of a cone is given by the formula:
V = (1/3)πr^2h

Substituting the values:
V = (1/3)π [(54 / π)^(1/3)]^2 2 (54 / π)^(1/3)

Simplifying further: