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?
To find the volume of the cylinder, we need to first find the radius of the sphere.
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 rearrange the formula to solve for the radius:
48 = (4/3)πr^3
r^3 = (3/4)*(48/π)
r^3 = 36
r = 3
So, the radius of the sphere is 3 meters.
Given that the height of the cylinder is equal to the diameter of the sphere, which is 2 times the radius:
Height of the cylinder = 2 * 3 = 6 meters
Now, we can calculate the volume of the cylinder using the formula V = πr^2h, where r is the radius of the cylinder and h is the height of the cylinder:
V = π*(3)^2*(6)
V = 54π
Therefore, the volume of the cylinder is 54π or approximately 169.65 m^3.