1. 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)
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. Since the volume of the sphere is given as 48 m^3, we can solve for r:
48 = (4/3)πr^3
48 * 3/4π = r^3
36/π = r^3
r^3 = 36/π
r = (36/π)^(1/3)
The height of the cylinder is equal to the sphere's diameter, which is twice the radius. Therefore, the height of the cylinder is 2r.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the cylinder and h is the height. Substituting the values we obtained:
V = π[(36/π)^(1/3)]^2 * 2[(36/π)^(1/3)]
= π(36/π)^(2/3) * 2(36/π)^(1/3)
= 2π(36/π) * (36/π)^(1/3)
= 2 * 36^(1/3) * π^(2/3)
Therefore, the volume of the cylinder is 2 * 36^(1/3) * π^(2/3).