A medicine capsule is a cylinder with a hemisphere closing each end, and every part has radius 3 mm. The capsule measures 15 mm from tip to tip. Find its volume in ${\text{mm}}^3$, in terms of π.

Each hemisphere adds 3 mm to the length, so the cylinder inside is 15 − 3 − 3 = 9 mm long. Cylinder = π$(3^2)(9)=81$π ${\text{mm}}^3$; the two hemispheres together make one sphere = (4/3)π(27) = 36π ${\text{mm}}^3$. Total = 81π + 36π = 117π ${\text{mm}}^3$. (Taking the cylinder as the full 15 mm long double-counts the ends and gives 135π + 36π = 171π; 81π is the cylinder alone; treating each end as a whole sphere gives 81π + 72π = 153π.)