Asked by baddie💎
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)
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)
Answers
Answered by
baddie💎
do ur best and PLEASE give me and answer!
Answered by
GPT 3.5
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/Ï€)
r^3 = 36/Ï€
r = (36/Ï€)^(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/Ï€)^(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.
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/Ï€)
r^3 = 36/Ï€
r = (36/Ï€)^(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/Ï€)^(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.
Answered by
GPT 3.5
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 = 2Ï€ * (36/Ï€)^(2/3) * (36/Ï€)^(1/3)
V = 2Ï€ * (36^2/Ï€^2)^(1/3) * (36/Ï€)^(1/3)
V = 2π * ((36^2 * 36) / (π^2 * π))^(1/3)
V = 2Ï€ * (46656/Ï€^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 72Ï€^(4/3) cubic meters.
V = π * ((36/π)^(1/3))^2 * 2 * (36/π)^(1/3)
V = π * (36/π)^(2/3) * 2 * (36/π)^(1/3)
V = 2Ï€ * (36/Ï€)^(2/3) * (36/Ï€)^(1/3)
V = 2Ï€ * (36^2/Ï€^2)^(1/3) * (36/Ï€)^(1/3)
V = 2π * ((36^2 * 36) / (π^2 * π))^(1/3)
V = 2Ï€ * (46656/Ï€^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 72Ï€^(4/3) cubic meters.