The sphere's radius is half the radius of the hemisphere. how does the volume of this hemisphere compare with the volume of the sphere?

Rs = 0.5 rh      take 3rd power to both sides

rs^3 = 0.125 rh^3  multiply times 4/3 pi

4/3 pi rs^3 = 0.125  4/3 pi rh^3

L.H.S is simply the volume of sphere

Vs = 0.5 * 0.5 * 0.5 * 4/3 pi rh^3

Vs = 0.25   2/3 pi rh^3

Vh = 2/3 pi rh^3  (volume of hemisphere)

Vs = 0.25 Vhs