Question

The volume of a sphere is 48 m3 . 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]

To find the volume of a cylinder, we need to know the radius and the height of the cylinder.

Given that the radius of the cylinder is the same as the sphere's, we can use the formula for the volume of a sphere to find the radius.

The volume of a sphere is given by the formula V = (4/3)πr³, where V is the volume and r is the radius.

Let's solve for r:
48 m³ = (4/3)πr³

Divide both sides of the equation by (4/3)π:
r³ = (3/4) * 48 / π

Simplify the right side:
r³ = 36 / π

Take the cube root of both sides:
r = (36 / π)^(1/3)

Now that we have the radius, we can find the height of the cylinder. The height of the cylinder is equal to the sphere's diameter, which is twice the radius.

So, the height of the cylinder is 2r.

Now we can calculate the volume of the cylinder using the formula for the volume of a cylinder, V = πr²h:
V_cylinder = π * r² * (2r)

Simplify:
V_cylinder = 2π * r³

Substitute the value of r we found earlier:
V_cylinder = 2π * ((36 / π)^(1/3))³

Calculate the cube:
V_cylinder = 2π * (36 / π)^((1/3)*3)

Simplify:
V_cylinder = 2π * (36 / π)

Simplify further:
V_cylinder = 72 m³

Therefore, the volume of the cylinder is 72 m³.