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Maths · Grade 5 · Set B
Cubes in a box
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B
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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 centimeter on every side. The box is full of cubes. What is its volume in cubic centimeters?
2
The box is one layer of cubes. What is its volume in cubic units?
3
Each cube is 1 foot on every side. What unit measures the volume of this box?
square feetfeetcubic feet
4
Count every cube, even the hidden ones at the back. What is the volume in cubic units?
5
Which box holds 18 unit cubes?
A
B
C
6
A box that is 6 cubes long, 2 cubes wide and 3 cubes tall holds 36 cubes.
TrueFalse

Layers and mistakes

7
The volume of this box is 9 cubic units.
TrueFalse
8
The top layer of this box has 8 cubes. The box has 4 layers. How many cubes are in the box in all?
9
The box is 2 cubes long, 2 cubes wide and 6 cubes tall. What is the volume in cubic units?
10
Join each box to its volume.
  1. 13 long, 2 wide, 1 tall
  2. 24 long, 3 wide, 1 tall
  3. 33 long, 3 wide, 3 tall
  4. 45 long, 2 wide, 3 tall
  • A12 cubic units
  • B27 cubic units
  • C6 cubic units
  • D30 cubic units
11
Put the boxes in order from the smallest volume to the greatest volume.
  • 4 by 3 by 3
  • 3 by 2 by 2
  • 2 by 2 by 1
  • 2 by 3 by 3
12
Sam says this box holds 3 + 2 + 2 = 7 cubes. What mistake did he make?
There is no mistake.He counted one layer too many.He added the sides. One layer has 3 × 2 = 6 cubes, and 2 layers hold 12.
13
Explain how to find the volume of a box 4 long, 3 wide and 2 tall without counting every cube.
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Answer key · Set B
Cubes in a box
14 Count the cubes: 2 along the front and 2 deep make 4 cubes. Each cube is one cubic centimeter.
210 One layer of 5 × 2 cubes is 10 cubes.
3cubic feet Volume counts cubes, so it is measured in cubic units: cubic feet. Feet measure length and square feet measure area.
420 One layer has 5 × 2 = 10 cubes. There are 2 layers, so 20 cubes.
5B Box A holds 4 × 2 × 2 = 16 cubes, box B holds 3 × 2 × 3 = 18 and box C holds 3 × 3 × 3 = 27.
6True One layer has 6 × 2 = 12 cubes, and 3 layers hold 36.
7False Do not add 4 + 2 + 3. One layer has 4 × 2 = 8 cubes. There are 3 layers, so the volume is 24 cubic units.
832 Every layer has the same number of cubes. 8 + 8 + 8 + 8 = 32.
924 One layer has 2 × 2 = 4 cubes. There are 6 layers, so 6 × 4 = 24 cubes.
101-C, 2-A, 3-B, 4-D
114, 2, 1, 3 Multiply each one: 4, 12, 18 and 36 cubic units.
12He added the sides. One layer has 3 × 2 = 6 cubes, and 2 layers hold 12. Volume is the number of cubes, found by multiplying: one layer of 6 cubes, 2 layers, so 12 cubic units.
13Your own words: a grown-up reads it.
Mark each answer, count the right ones and write the score on the sheet.