### Instruction: A sphere is inscribed inside a hemisphere of radius 2.  What is the volume of this sphere?### Response: A sphere is inscribed inside a hemisphere of radius 2 means that the sphere touches the hemisphere at the base and at the center of the curved surface.
This implies that the diameter of the sphere is equal to the radius of the hemisphere, which is 2.
Therefore, the radius of the sphere is 1.
The volume of a sphere with radius r is given by the formula V = (4/3)πr^3.
Plugging in r = 1, we get V = (4/3)π(1)^3 = (4/3)π.