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Maths · Grade 5 · Set A
Counting cubes
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A
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Goal: 15 min
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Remember: A unit cube has a volume of one cubic unit. Count the cubes, even the hidden ones, or count one layer and multiply by the number of layers.

Count the unit cubes

1
Each cube is 1 inch on every side. The box is full of cubes. What is its volume in cubic inches?
2
Each cube is 1 foot on every side. Count the cubes in the box. What is its volume in cubic feet?
3
Each cube is 1 inch on every side. What unit measures the volume of this box?
cubic inchesinchessquare inches
4
Count every cube, even the hidden ones at the back. What is the volume in cubic units?
5
Which box holds 12 unit cubes?
A
B
C
6
A box that is 5 cubes long, 4 cubes wide and 2 cubes tall holds 40 cubes.
TrueFalse

Layers and mistakes

7
The volume of this box is 12 cubic units.
TrueFalse
8
The top layer of this box has 12 cubes. The box has 3 layers. How many cubes are in the box in all?
9
The box is one layer of cubes. What is its volume in cubic units?
10
The cubes are packed in a box shaped like a cube, 3 long, 3 wide and 3 tall. What is the volume in cubic units?
11
Join each box to its volume.
  1. 12 long, 2 wide, 2 tall
  2. 23 long, 3 wide, 1 tall
  3. 34 long, 2 wide, 2 tall
  4. 45 long, 2 wide, 2 tall
  • A9 cubic units
  • B20 cubic units
  • C16 cubic units
  • D8 cubic units
12
Put the boxes in order from the smallest volume to the greatest volume.
  • 3 by 3 by 2
  • 4 by 3 by 2
  • 2 by 2 by 2
  • 2 by 2 by 3
13
Mia counted the 12 little squares on the faces she can see and said the volume is 12 cubic units. What mistake did she make?
She forgot to count the top layer.She counted squares on the faces, not cubes.She counted a cube twice.
14
Explain why volume is measured in cubic units and not square units.
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Answer key · Set A
Counting cubes
16 Count the cubes: 2 along the bottom and 3 layers make 6 cubes. Each cube is one cubic inch.
212 Each layer has 3 × 2 = 6 cubes. There are 2 layers, so 12 cubes. The volume is 12 cubic feet.
3cubic inches Volume counts cubes, so it is measured in cubic units. Inches measure length and square inches measure area.
424 One layer has 4 × 3 = 12 cubes. There are 2 layers, so 24 cubes.
5C Box A holds 4 × 2 × 2 = 16 cubes and box B holds 2 × 2 × 2 = 8. Box C holds 3 × 2 × 2 = 12.
6True One layer has 5 × 4 = 20 cubes, and 2 layers hold 40.
7False One layer has 3 × 3 = 9 cubes. There are 2 layers, so the volume is 18 cubic units.
836 Every layer has the same number of cubes. 12 + 12 + 12 = 36.
915 One layer of 5 × 3 cubes is 15 cubes.
1027 One layer has 3 × 3 = 9 cubes, and 3 layers make 27.
111-D, 2-A, 3-C, 4-B
123, 4, 1, 2 Multiply each one: 8, 12, 18 and 24 cubic units.
13She counted squares on the faces, not cubes. Faces are not cubes. The box has 2 layers of 4 cubes, so the volume is 8 cubic units.
14Your own words: a grown-up reads it.
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