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Maths · Grade 6 · Set C
Fraction Edges and Joined Boxes
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C
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Goal: 15 min
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Remember: Small cubes fill a box with fraction edges. Count them, or multiply the edges (or base × height): it is the same volume.

Pack the box

1
This box is packed with half-inch cubes, 6 long, 4 wide and 5 high. How many half-inch cubes fill it?
2
8 half-inch cubes fill 1 cubic inch. What is the volume of that box in cubic inches?
120 cubic inches60 cubic inches15 cubic inches
3
A crate is 1 1/2 feet long, 1 foot wide and 2 feet high. The picture shows it packed with half-foot cubes. What is its volume in cubic feet?
4
Each small cube is one third unit on every side. Which box has the greatest volume?
Box 1
Box 2
Box 3
5
A box is 2 1/2 meters long, 2 meters wide and 1/5 meter high. What is its volume in cubic meters?
6
The base of a box has an area of 3/4 square foot. The box is 8 feet high. What is its volume?
6 cubic feet8 3/4 cubic feet3/32 cubic foot

Think about volume

7
The base of a box has an area of 5/6 square meter. The box is 3/5 meter high. What is its volume in cubic meters? Write a fraction.
8
A cube with every edge 1/4 unit has a volume of 1/12 cubic unit.
TrueFalse
9
Why do 8 half-unit cubes fill one cubic unit, and not 4?
Because 2 × 2 = 4, and the height does not count.Because half of 16 is 8.Because 2 × 2 × 2 = 8: 2 across, 2 deep and 2 high.
10
Join each box to its volume.
  1. 11/2 × 1/2 × 1/2
  2. 21/2 × 1/2 × 2
  3. 31/3 × 3 × 2
  4. 43/4 × 1/2 × 2
  • A1/2
  • B2
  • C1/8
  • D3/4
11
Two boxes make one solid. Both are packed with half-unit cubes, and 8 half-unit cubes fill 1 cubic unit. What is the volume of the solid in cubic units? Write a fraction.
12
Packing a box with small cubes gives a different volume than multiplying its edges.
TrueFalse
13
A box is 1 1/2 feet long, 1 foot wide and 1 foot high. Write how you can use half-foot cubes to find its volume.
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Answer key · Set C
Fraction Edges and Joined Boxes
1120 6 × 4 = 24 in a layer, and 5 layers: 24 × 5 = 120.
215 cubic inches 120 cubes shared 8 to a cubic inch is 120 ÷ 8 = 15.
33 3 × 2 × 4 = 24 cubes, and 8 of them make a cubic foot: 24 ÷ 8 = 3. Or 3/2 × 1 × 2 = 3.
4Box 3 Count the cubes. Box 1 has 4 × 3 × 3 = 36, Box 2 has 6 × 2 × 3 = 36 and Box 3 has 3 × 3 × 5 = 45, the most.
51 2 1/2 is 5/2. Then 5/2 × 2 = 5, and 5 × 1/5 = 1.
66 cubic feet Volume is base × height: 3/4 × 8 = 24/4 = 6 cubic feet.
71/2 Volume is base × height: 5/6 × 3/5 = 15/30, which is 1/2.
8False 4 × 4 × 4 = 64 quarter-unit cubes fill 1 cubic unit, so each is 1/64. Also 1/4 × 1/4 × 1/4 = 1/64.
9Because 2 × 2 × 2 = 8: 2 across, 2 deep and 2 high. There are 2 layers of 4 cubes. The height counts too.
101-C, 2-A, 3-B, 4-D Multiply the three edges: 1/8, 1/2, 2 and 3/4.
115/2 3 × 2 × 2 = 12 cubes and 2 × 2 × 2 = 8 cubes make 20 cubes. 20 ÷ 8 = 20/8, which is 5/2.
12False Both ways find the same volume. Counting 12 half-unit cubes is 12/8 = 3/2, and 1 × 3/2 × 1 = 3/2.
13Your own words: a grown-up reads it.
Mark each answer, count the right ones and write the score on the sheet.