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Maths · Grade 6 · Set A
Filling a Box With Little 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 half-unit cubes. How many cubes fill it?
2
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?
3
This box is packed with half-inch cubes, 4 long, 3 wide and 3 high. How many half-inch cubes fill it?
4
8 half-inch cubes fill 1 cubic inch. What is the volume of this box in cubic inches? Write a fraction.
5
A box one half foot long, 1 foot wide and one half foot high has a volume of 1/4 cubic foot.
TrueFalse
6
Half-meter cubes make this box 3 meters long, one half meter wide and one half meter high. What is its volume in cubic meters?
7
Each small cube is one half unit on every side. Which box has a volume of 1 cubic unit?
Box 1
Box 2
Box 3
8
Join each little cube to how many of them fill one cubic unit.
  1. 1half-unit cubes
  2. 2quarter-unit cubes
  3. 3third-unit cubes
  • A64 cubes
  • B8 cubes
  • C27 cubes
9
This box is packed with 54 third-unit cubes. 27 third-unit cubes fill 1 cubic unit. What is the volume in cubic units?
10
Each small cube is one half unit on every side. What is the volume of this box in cubic units? Write a fraction.
11
A box is 3/4 foot long, 1/2 foot wide and 4 feet high. Multiply the edges. What is the volume in cubic feet? Write a fraction.
12
To find the volume of a box, multiply only the length and the width.
TrueFalse
13
A box is 1 meter long, 3 meters wide and 5/2 meters high. What is its volume in cubic meters? Write a fraction.
14
A box is 1 unit on every side. Write how you know 8 half-unit cubes fill it, and what each little cube is of a cubic unit.
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Answer key · Set A
Filling a Box With Little Cubes
18 2 cubes across, 2 deep and 2 high: 2 × 2 × 2 = 8.
264 One layer is 4 × 4 = 16 cubes and there are 4 layers: 64.
336 4 × 3 = 12 in a layer, and 3 layers: 36.
49/2 36 cubes shared 8 to a cubic inch is 36 ÷ 8 = 9/2, which is 4 and a half.
5True Its edges are 1/2, 1 and 1/2, and 1/2 × 1 × 1/2 = 1/4. Two half-foot cubes of 1/8 each also make 1/4.
63/4 It takes 6 half-meter cubes, and each is 1/8 of a cubic meter. 6/8 is 3/4.
7Box 2 8 half-unit cubes fill 1 cubic unit. Box 2 has 8 cubes, Box 1 has 4 and Box 3 has 16.
81-B, 2-A, 3-C Across × deep × high: 2 × 2 × 2, 4 × 4 × 4 and 3 × 3 × 3.
92 54 cubes shared 27 to a cubic unit is 54 ÷ 27 = 2.
1015/4 5 × 3 × 2 = 30 cubes, and 8 cubes make 1 cubic unit. 30/8 = 15/4.
113/2 3/4 × 1/2 = 3/8, and 3/8 × 4 = 12/8 = 3/2.
12False That gives one layer, the base. The height counts too: length × width × height.
1315/2 1 × 3 = 3, and 3 × 5/2 = 15/2.
14Your own words: a grown-up reads it.
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