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?

(1 point)

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 r is the radius of the sphere.

Given that the volume of the sphere is 48 m^3, we can rearrange the formula to solve for the radius:
48 = (4/3)πr^3
r^3 = 48 * 3 / 4π
r^3 = 36 / π
r = (36 / π)^(1/3)

Now, the height of the cylinder is equal to the sphere's diameter, which means it is equal to twice the radius: h = 2r.

Therefore, the volume of the cylinder can be calculated using the formula V = πr^2h:
V = π((36 / π)^(1/3))^2 * 2(36 / π)^(1/3)
V = π(36 / π)^(2/3) * 2(36 / π)^(1/3)
V = 72

Therefore, the volume of the cylinder is 72 m^3.