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Maths · Grade 6 · Set B
Third-Unit and Half-Foot Cubes
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Remember: Small cubes fill a box with fraction edges. Count them, or multiply the edges: it is the same volume.

Pack the box

1
A box is 1 unit long, 1 unit wide and 1 unit high. It is packed with third-unit cubes. How many cubes fill it?
2
This box is packed with half-foot cubes, 3 long, 3 wide and 2 high. How many half-foot cubes fill it?
3
8 half-foot cubes fill 1 cubic foot. What is the volume of that box in cubic feet? Write a fraction.
4
A cube that is 1/2 foot on every edge has a volume of 1/8 cubic foot.
TrueFalse
5
Third-unit cubes fill this box, 5 long, 3 wide and 3 high. 27 third-unit cubes fill 1 cubic unit. What is the volume in cubic units? Write a fraction.
6
Each small cube is one half unit on every side. Which box has a volume of 2 cubic units?
Box 1
Box 2
Box 3
7
Join each little cube to how many of them fill one cubic unit.
  1. 1fifth-unit cubes
  2. 2sixth-unit cubes
  3. 3eighth-unit cubes
  4. 4tenth-unit cubes
  • A216 cubes
  • B1,000 cubes
  • C125 cubes
  • D512 cubes

Multiply the edges

8
A box is 1/2 meter long, 3/5 meter wide and 4 meters high. Multiply the edges. What is the volume in cubic meters? Write a fraction.
9
To find the volume of a box with fraction edges, multiply its length, its width and its height.
TrueFalse
10
A box is packed with 40 half-inch cubes. 8 half-inch cubes fill 1 cubic inch. What is the volume of the box?
5 cubic inches40 cubic inches8 cubic inches
11
Multiply the edges. Number the boxes from the smallest volume (1) to the largest (4).
  • 1 × 1 × 3/4
  • 2 × 1/2 × 1
  • 1/2 × 1/2 × 2
  • 3/2 × 1/2 × 2
12
This box is packed with quarter-unit cubes, 6 long, 4 wide and 4 high. 64 quarter-unit cubes fill 1 cubic unit. What is the volume in cubic units? Write a fraction.
13
A box is 1 unit on every side. Write how many third-unit cubes fill it, and what fraction of a cubic unit each little cube is.
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Answer key · Set B
Third-Unit and Half-Foot Cubes
127 3 cubes across, 3 deep and 3 high: 3 × 3 × 3 = 27.
218 3 × 3 = 9 in a layer, and 2 layers: 18.
39/4 18 cubes shared 8 to a cubic foot is 18 ÷ 8 = 18/8, which is 9/4, or 2 and a quarter.
4True 1/2 × 1/2 × 1/2 = 1/8. Eight of them fill one cubic foot.
55/3 5 × 3 × 3 = 45 cubes. 45 cubes shared 27 to a cubic unit is 45/27, which is 5/3.
6Box 3 8 half-unit cubes fill 1 cubic unit, so 2 cubic units need 16 cubes. Box 3 has 2 × 4 × 2 = 16. Box 1 has 12 and Box 2 has 24.
71-C, 2-A, 3-D, 4-B Across × deep × high: 5 × 5 × 5, 6 × 6 × 6, 8 × 8 × 8 and 10 × 10 × 10.
86/5 1/2 × 3/5 = 3/10, and 3/10 × 4 = 12/10, which is 6/5.
9True The volume is length × width × height, whether the edges are whole numbers or fractions.
105 cubic inches 40 cubes shared 8 to a cubic inch is 40 ÷ 8 = 5.
112, 3, 1, 4 The volumes are 1/2, 3/4, 1 and 3/2.
123/2 6 × 4 × 4 = 96 cubes. 96 cubes shared 64 to a cubic unit is 96/64, which is 3/2.
13Your own words: a grown-up reads it.
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