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?

Answer 1

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.