Volume and Unit Cubes

Mathematics · Measurement · ages 10-11

Name ______________________ Date ____________

A unit cube has sides of length 1 unit. How much volume does it have?
- 1 cubic unit
- 1 square unit
- 2 cubic units
A solid is packed with 36 unit cubes and no gaps. What is its volume in cubic units?
Answer: ______________
A unit cube has sides of 1 unit. What is its volume?
- 1 cubic unit
- 1 square unit
- 1 unit
- 6 cubic units
What does 'volume' tell you about a 3D shape?
- How much space it takes up
- How long one side is
- How flat its surface is
Which job needs volume: filling a box with cubes or wrapping it with paper?
- Filling a box with cubes
- Wrapping a box with paper
- Measuring the edge
- Counting the faces
Which unit is used to measure volume?
- Square units
- Cubic units
- Just units
A box face has area 20 cm². The whole box has volume 100 cm³. Which statement is true?
- Area covers a face, volume fills the box
- Area and volume are the same thing
- Volume is always the bigger number
- Area uses cubic units
This solid is built from two layers of unit cubes, 3 cubes in each layer. What is its total volume?
- 3 cubic units
- 6 cubic units
- 9 cubic units
Ben built a solid from 9 unit cubes but says its volume is 9 square units. What's his mistake?
- He counted wrong; it's really 3 cubic units
- Square units and cubic units mean the same thing
- He should say 9 cubic units, since volume uses cubic units
A solid is built in 3 layers: 4 cubes, 4 cubes, and 2 cubes. What is the total volume?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

1 cubic unit · A unit cube is the basic building block for volume: it always equals exactly 1 cubic unit.
36 · 36 unit cubes with no gaps means 36 cubic units.
1 cubic unit · One unit cube fills exactly one cubic unit of space.
How much space it takes up · Volume measures the space filled by a solid shape, not just one side's length.
Filling a box with cubes · Filling uses cubes (volume); wrapping covers faces (surface area).
Cubic units · Volume is measured in cubic units, because it fills 3D space, not a flat surface.
Area covers a face, volume fills the box · The 20 cm² face is flat cover; the 100 cm³ fills the box. Different jobs.
6 cubic units · Add the cubes in each layer: 3 + 3 = 6 cubic units.
He should say 9 cubic units, since volume uses cubic units · The count of 9 is right, but the unit is wrong. Volume always uses cubic units, not square units.
10 · Add every layer: 4 + 4 + 2 = 10 cubic units.