The volume of a sphere is 48 M squared what is the volume of a cylinder if its radius is the same as his fears, and its height is equal to the spheres diameter?
Let's solve this step by step:
Given:
Volume of sphere = 48 cubic meters
Step 1: Find the radius of the sphere.
The formula for the volume of a sphere is V = (4/3)πr^3.
48 = (4/3) * π * r^3
Multiply both sides by 3/4 to isolate the radius, r:
r^3 = (48 * 3) / (4π)
r^3 = 36 / π
Take the cube root of both sides:
r = ∛(36 / π)
r ≈ 2.163 meters
Step 2: Find the diameter of the sphere.
The diameter of a sphere is twice its radius.
Diameter = 2 * radius = 2 * 2.163 ≈ 4.326 meters
Step 3: Find the height of the cylinder.
Given that the height of the cylinder is equal to the diameter of the sphere, the height of the cylinder is 4.326 meters.
Step 4: Find the volume of the cylinder.
The formula for the volume of a cylinder is V = πr^2h.
Substituting the given values:
V = π * (2.163)^2 * 4.326
V ≈ 62.742 cubic meters
Therefore, the volume of the cylinder is approximately 62.742 cubic meters.