A flat semicircular sheet of radius 6 cm is spun rapidly about its straight edge. Find the volume of the solid it sweeps out, in ${\text{cm}}^3$, in terms of π.

The straight edge is a diameter, so a half-turn already sweeps a full sphere of radius 6 cm: volume = (4/3)π$(6^3)=$ (4/3)π × 216 = 288π ${\text{cm}}^3$. (144π is a hemisphere, which is what a QUARTER circle would sweep; 216π is π$r^3$, dropping the 4/3; 72π is the cone (1/3)π$(6^2)$(6), the solid swept by a right triangle, not by a semicircular sheet.)