A cylinder and a sphere both have the same radius r, where r > 0. The (May 2023 U.S.)

Correct answer: 6.
Let's start by finding the volume of the cylinder. The formula for the volume of a cylinder is:
V_cylinder = πr^2h

where r is the radius and h is the height. In this case, the height is 16, so:
V_cylinder = πr^2(16) = 16πr^2

The volume of the sphere is half the volume of the cylinder, so:
V_sphere = 1/2(16πr^2) = 8πr^2

We know that the sphere and cylinder have the same radius, so we can set up an equation using the formula for the volume of a sphere:
V_sphere = (4/3)πr^3

Equating this to the volume of the sphere we found earlier, we get:
8πr^2 = (4/3)πr^3

Dividing both sides by πr^2, we get:
8 = (4/3)r

Multiplying both sides by 3, we get:
24 = 4r

Dividing both sides by 4, we get:
r = 6