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)

m^3

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this problem, we first need to 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.

In this case, the volume of the sphere is 48 m^3.

48 = (4/3)πr^3

To find the radius, we can solve for r.

r^3 = (3/4)(48/π) = 3(16/π) = 48/π

r = (48/π)^(1/3)

Now, the height of the cylinder is equal to the sphere's diameter, which is twice the radius.

Height of cylinder = 2r = 2(48/π)^(1/3)

The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.

Therefore, the volume of the cylinder is:

V = π(48/π)^(1/3)^2 * 2(48/π)^(1/3)

Simplifying this expression, we get:

V = 2 * 48/π = 96/π

So, the volume of the cylinder is 96/π m^3.