Part 1 of 8
800 point giveaway
Part one
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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