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Maths · Grade 5 · Set C
Volume by layers
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C
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Goal: 15 min
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Remember: A unit cube has a volume of one cubic unit. Count one layer, then multiply by the number of layers, and volume adds when boxes are joined.

Count by layers

1
Each cube is 1 inch on every side. What is the volume of this box in cubic inches?
2
Count by layers, even the hidden ones. What is the volume in cubic units?
3
This is one layer of a box. The box holds 30 cubes in all. How many layers does the box have?
4
A box holds 24 cubes in 3 equal layers. How many cubes are in one layer?
5
The box above holds the same number of cubes as one of these boxes. Which one?
A
B
C

Use volume

6
A box 2 cubes long, 3 wide and 4 tall holds the same number of cubes as a box 4 long, 3 wide and 2 tall.
TrueFalse
7
A toy box is 4 feet long, 4 feet wide and 3 feet tall. It is packed with cubes that are 1 foot on every side. What is its volume in cubic feet?
8
Each cube is 1 meter on every side. What unit measures the volume of this box?
meterscubic meterssquare meters
9
Two boxes are joined to make one bigger box. The first holds 12 cubes and the second holds 18 cubes. How many cubes do the two boxes hold in all?
10
Count by layers. What is the volume of this tall box in cubic units?
11
Join each stack of layers to its volume.
  1. 13 layers of 8 cubes
  2. 22 layers of 15 cubes
  3. 34 layers of 9 cubes
  4. 46 layers of 7 cubes
  • A24 cubic units
  • B42 cubic units
  • C30 cubic units
  • D36 cubic units
12
Put the boxes in order from the smallest volume to the greatest volume.
  • 4 by 4 by 3
  • 6 by 3 by 3
  • 3 by 2 by 4
  • 5 by 3 by 2
13
Max says a box with 3 layers of 10 cubes holds 13 cubes. What mistake did Max make?
He added 10 + 3. He should multiply: 3 × 10 = 30 cubes.He forgot to count the top layer.There is no mistake.
14
Pip says volume and area mean the same thing. Write what is different. Use the words square units and cubic units.
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Answer key · Set C
Volume by layers
130 One layer has 5 × 2 = 10 cubes. There are 3 layers, so 30 cubes.
245 One layer has 5 × 3 = 15 cubes. 3 layers hold 15 + 15 + 15 = 45.
32 One layer has 5 × 3 = 15 cubes. 15 + 15 = 30, so there are 2 layers.
48 24 cubes shared among 3 layers is 8 cubes in each layer.
5B The box above holds 4 × 3 × 2 = 24 cubes. Box B holds 2 × 3 × 4 = 24. Box A holds 27 and box C holds 32.
6True 2 × 3 × 4 = 24 and 4 × 3 × 2 = 24. The same cubes can be stacked in a different shape.
748 One layer has 4 × 4 = 16 cubes. 3 layers hold 48, so the volume is 48 cubic feet.
8cubic meters Volume counts cubes, so it is measured in cubic meters. Meters measure length and square meters measure area.
930 Volume adds: 12 + 18 = 30 cubes.
1060 One layer has 4 × 3 = 12 cubes. 5 layers hold 5 × 12 = 60 cubes.
111-A, 2-C, 3-D, 4-B
123, 4, 1, 2 Multiply each one: 24, 30, 48 and 54 cubic units.
13He added 10 + 3. He should multiply: 3 × 10 = 30 cubes. Every layer holds 10 cubes, and there are 3 layers, so the box holds 3 × 10 = 30 cubes.
14Your own words: a grown-up reads it.
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