The largest possible sphere is carved out of a solid wooden cube of edge 21 cm. What volume of wood is wasted, in cubic cm? (Use π = 22/7.)

The largest sphere has a diameter equal to the cube's edge, so $r=10.5$ cm and its volume = $(4/3)\times (22/7)\times 10.5^3=(4/3)\times 3638.25=4851$ cubic cm. The cube is $21^3=9261$ cubic cm, so the wood wasted = 9261 - 4851 = 4410 cubic cm. The trap 4851 gives the sphere that is KEPT rather than the offcut; 9261 is the whole block; 5622.75 subtracts π$r^3=3638.25$, dropping the 4/3 from the sphere's volume.