The volume of a sphere is 48m ^ 3 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 given by the formula: V = (4/3)πr^3.
We are told that the volume of the sphere is 48 m^3. Let's solve for r.
48 = (4/3)πr^3
48 * (3/4π) = r^3
36π = r^3
To find the volume of a cylinder with the same radius as the sphere and a height equal to the sphere's diameter, we need to find the diameter first.
The diameter of a sphere is given by the formula: d = 2r.
Therefore, the diameter of the sphere is 2 * r = 2 * ∛(36π).
The height of the cylinder is equal to the sphere's diameter, so h = 2 * ∛(36π) as well.
The volume of a cylinder is given by the formula: V = πr^2h.
Substituting the values, we get:
V = π * r^2 * (2 * ∛(36π))
The radius of the cylinder is the same as the sphere, so we have:
V = π * (∛(36π))^2 * (2 * ∛(36π))
V = π * 36 * 2
V = 72π
The volume of the cylinder is 72π cubic meters.