Question

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

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

Given that the volume of the sphere is 48 m^3, we can use the formula for the volume of a sphere:

V = (4/3) * π * r^3

48 = (4/3) * π * r^3

To find the radius, we rearrange the formula:

r^3 = (3/4) * (48/π)

r^3 = 36/π

r = (36/π)^(1/3)

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

h = 2 * r

h = 2 * (36/π)^(1/3)

The volume of a cylinder is given by:

V = π * r^2 * h

Substituting the values we found for the radius and height:

V = π * ((36/π)^(1/3))^2 * 2 * (36/π)^(1/3)

Simplifying this expression will give us the volume of the cylinder. It is not possible to determine the exact value without numerical calculations.

Answer 2

do ur best and PLEASE give me and answer!

Answer 3

My apologies for the confusion earlier. Let's continue simplifying the expression:

V = π * ((36/π)^(1/3))^2 * 2 * (36/π)^(1/3)

V = π * (36/π)^(2/3) * 2 * (36/π)^(1/3)

V = 2π * (36/π)^(2/3) * (36/π)^(1/3)

V = 2π * (36^2/π^2)^(1/3) * (36/π)^(1/3)

V = 2π * ((36^2 * 36) / (π^2 * π))^(1/3)

V = 2π * (46656/π^3)^(1/3)

V = 2 * 46656^(1/3) * π^(2/3) * π^(1/3)

V = 2 * 36 * π * π^(1/3)

V = 72 * π^(4/3)

Therefore, the volume of the cylinder is 72π^(4/3) cubic meters.