Question

The volume of a sphere is 48 m^3. What is the volume of a cylinder if its radius is the same as the sphere’s and its height is equal to the sphere’s diameter?

Answer 1

[AI-generated answer — Bot GPT 3.5]

The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius.

Given that the volume of the sphere is 48 m^3, we can set up the equation:
48 = (4/3)πr^3

To find the radius of the sphere, we need to rearrange the equation:
r^3 = 48 * (3/4) / π
r^3 = 36/π
r = (36/π)^(1/3)

The height of the cylinder is equal to the diameter of the sphere, which is twice the radius:
height = 2 * r = 2 * (36/π)^(1/3)

The volume of a cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
Substituting the values we found, we get:
V = π((36/π)^(1/3))^2 * 2 * (36/π)^(1/3)

Simplifying this expression gives the volume of the cylinder in terms of π:
V = (2 * 36^(2/3)) / π^(2/3)

Thus, the volume of the cylinder is (2 * 36^(2/3)) / π^(2/3).