The volume of a sphere is 48 m^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, where r is the radius of the sphere.
Given that the volume of the sphere is 48 m^3, we can set up the following equation:
48 = (4/3)πr^3
Solving for the radius r, we get:
r^3 = 36 / π
r = (36 / π)^(1/3)
Now, the volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
Since the radius of the cylinder is the same as the sphere's and the height is equal to the sphere's diameter, the height of the cylinder is 2r.
Therefore, the volume of the cylinder is:
V_cylinder = πr^2 * 2r = 2πr^3
Substitute the radius r that we found earlier:
V_cylinder = 2π(36 / π)^(1/3)
V_cylinder = 2(36)^(1/3) = 2*3 = 6 m^3
Therefore, the volume of the cylinder is 6 m^3.