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) m3

Answer 1

To find the volume of the cylinder, we need to first determine its dimensions.

Given that the radius of the cylinder is the same as the sphere, we'll call it r.

And the height of the cylinder is equal to the sphere's diameter, which is 2r.

The volume of a cylinder is given by the formula V = πr²h.

Substituting the values, V = πr²(2r).

Simplifying, V = 2πr³.

Since the volume of the sphere is given as 48 m³, we equate it to 2πr³ and solve for r:

48 = 2πr³.

Dividing both sides by 2π, we get r³ = 48/(2π).

Taking the cube root of both sides, r = (48/(2π))^(1/3).

Now, we can substitute this value of r back into the expression for the volume of the cylinder:

V = 2πr³.

V = 2π * [(48/(2π))^(1/3)]³.

Simplifying, V = 2π * [(48/(2π))^1]³.

V = 2π * [24/π]³.

V = 2 * 24³.

V = 2 * 13824.

V = 27648.

The volume of the cylinder is 27648 m³. Answer: \boxed{27648}.