How it works
Small cubes with fraction edges can fill a box. Count them, or multiply the edges: it is the same volume.
A half-unit cube is 1/2 on each edge, so it takes 8 of them to make 1 cubic unit.
Multiply length times width times height, even when the edges are fractions.
Worked examples
Count the cubes
- A box takes 5 by 4 by 1 half-unit cubes.
- 5 × 4 × 1 = 20 cubes.
- Each cube is 1/8 of a cubic unit, so it is 20/8 = 2 1/2 cubic units.
Multiply the edges
- A box has edges 1 ft, 2/3 ft and 5/3 ft.
- 1 × 2/3 × 5/3 = 10/9.
- 10/9 is 1 1/9 cubic feet.
Same volume
- The same box counted by third-foot cubes gives 30 cubes.
- 30 cubes of 1/27 each is 30/27.
- 30/27 is 1 1/9: the same volume.
A taste of the worksheet
These are the first problems of set A. The printable sheet has many more, with an answer key.
- A box is 1 unit long, 1 unit wide and 1 unit high. It is packed with half-unit cubes. How many cubes fill it? ___
- A box 1 unit on every side is packed with quarter-unit cubes: 4 across, 4 deep and 4 high. How many cubes fill it? ___