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)
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.
do ur best and PLEASE give me and answer!
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.
To find the volume of the cylinder, we need to know its radius and height. Since the radius of the cylinder is the same as the sphere's, we can first find the radius of the sphere using its volume.
The formula for the volume of a sphere is given by:
V_sphere = (4/3) * π * r^3
Given that the volume of the sphere is 48 m^3, we can rearrange the formula to solve for the radius (r):
48 = (4/3) * π * r^3
To solve for r, divide both sides of the equation by (4/3) * π:
48 / ((4/3) * π) = r^3
Now, we have:
r^3 = 48 / ((4/3) * π)
Simplify the equation:
r^3 = 36 / π
To solve for r, take the cube root of both sides:
r = (∛(36 / π))
Now that we have the radius of the sphere, we can find the volume of the cylinder.
The formula for the volume of a cylinder is given by:
V_cylinder = π * r^2 * h
Given that the height of the cylinder is equal to the diameter of the sphere, which is twice the radius, we can write:
h = 2r
Substituting this value in the volume formula:
V_cylinder = π * r^2 * 2r
Simplifying further:
V_cylinder = 2 * π * r^3
Now, substituting the value of r we calculated earlier:
V_cylinder = 2 * π * (∛(36 / π))^3
Calculating this expression will give us the volume of the cylinder.