\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?
The radius of the sphere can be determined using the formula for the volume of a sphere:
V = (4/3) * π * r^3
48 = (4/3) * π * r^3
Dividing both sides by (4/3) * π:
36 = r^3
Taking the cube root of both sides:
r = 3
The height of the cylinder is equal to the sphere's diameter, which is twice the radius:
h = 2 * r = 6
The volume of the cylinder can be determined using the formula for the volume of a cylinder:
V = π * r^2 * h
V = π * 3^2 * 6
V = π * 9 * 6
V = 54π
Therefore, the volume of the cylinder is 54π cubic meters.