### Instruction: A sphere is inscribed inside a hemisphere of radius 2.  What is the volume of this sphere?### Response: To inscribe a sphere inside a hemisphere, the center of the sphere must coincide with the center of the hemisphere, and the radius of the sphere must be equal to half the radius of the hemisphere.
So the radius of the sphere is 2/2 = 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.
This is the volume of the sphere.