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

The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. We are given that the volume of the sphere is 48 m^3, so we can set up the equation:

48 = (4/3)πr^3

To solve for the radius, we can rearrange the equation:

r^3 = (3/4)(48/π)
r^3 = 36
r = ∛36
r ≈ 3.301

The height of the cylinder is equal to the sphere's diameter, which is twice the radius. So the height of the cylinder would be:

h = 2r
h ≈ 2(3.301)
h ≈ 6.602

To find the volume of the cylinder, we use the formula V = πr^2h:

V = π(3.301)^2(6.602)
V ≈ π(11)^2(6.602)
V ≈ π(121)(6.602)
V ≈ 2413.4π

Thus, the volume of the cylinder is approximately 2413.4π cubic meters.