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)
First, we need to find the radius of the sphere. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.
Given that the volume of the sphere is 48 m³, we have:
48 = (4/3)πr³
Solving for r, we get:
r³ = (3/4) * 48 / π
r = ∛(3 * 48 / 4π)
r = ∛36 / ∛(4π) = 3 m
So, the radius of the sphere is 3 m.
Now, we need to find the volume of the cylinder. The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height.
Given that the height of the cylinder is equal to the diameter of the sphere, which is 2 times the radius of the sphere, we have:
h = 2 * 3 = 6 m
Substitute the radius and height into the formula for the volume of the cylinder:
V = π * (3)² * 6
V = π * 9 * 6
V = 54π m³
Therefore, the volume of the cylinder is 54π m³.