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Grade 6 (age 11-12)

grade 6 Volume of Space Figures

Volume is the amount of space an object takes up. The volume of a cube with 1 cm edges is written 1 cm³ and read "1 cubic centimeter", and you can find a volume by counting how many of these unit cubes fit inside. Count the cubes along the length and the width of one layer, multiply by the number of layers, and you get the total, which is why the volume of a rectangular prism is length × width × height. A cube with 10 cm edges has a volume of 1000 cm³, the same as the 1 L printed on a milk carton.

Counting volume with cubes

🧱 Counting volume with cubes
①One unit cube with 1 cm edges has a volume of 1 cm³
②The picture lays the same number of cubes along the length and the width of the floor, then stacks layers on top
③At the start the floor is 3 cubes by 3 cubes with 3 layers, so 3 × 3 × 3 = 27 cubes and the volume is 27 cm³
④Multiply the number of cubes in one layer by the number of layers and you know the total without counting one by one
3
3

Volume of a rectangular prism

5
3
4
📦 Volume of a rectangular prism = length × width × height
①The bottom face holds (length × width) cubes, and that layer is stacked as many times as the height
②So the volume of a rectangular prism is length × width × height, which is also the area of the base × height
③At the start the length is 5, the width 3 and the height 4, so 5 × 3 × 4 = 60 and the volume is 60 cm³
④A cube has equal length, width and height, so its volume is edge × edge × edge
This box
5 × 3 × 4 = 60 cm³ = 0.06 L
The volume from the length, width and height (in cm) chosen above. Since 1000 cm³ is 1 L, dividing by 1000 gives liters.

Units of volume

🥛 1 L = 1000 cm³
①1 cm³ is the volume of a cube with 1 cm edges
②A cube with 10 cm edges holds 10 × 10 × 10 = 1000 unit cubes
③So 1 L = 1000 cm³, and 1 mL = 1 cm³
④A 200 mL carton of milk holds 200 cm³, and a 1 L bottle of water holds 1000 cm³

Summary

Volume of a rectangular prism
V = length × width × height
Also the area of the base × height
Volume of a cube
V = edge × edge × edge
A rectangular prism whose length, width and height are all equal
Units of volume
1 L = 1000 cm³ = 1000 mL
10 cm × 10 cm × 10 cm = 1000 cm³ = 1 L
🎯 Key points
①Volume is the space an object takes up, measured by how many 1 cm³ cubes fit inside
②Volume of a rectangular prism = length × width × height = area of the base × height
③Volume of a cube = edge × edge × edge
④1 L = 1000 cm³ and 1 mL = 1 cm³
⑤When changing units, first give all the edge lengths in the same unit

Examples & Unit Review

Example 1
Find the volume of a rectangular prism 6 cm long, 4 cm wide and 5 cm high.
1
Volume = length × width × height = 6 × 4 × 5.
2
The base area 6 × 4 = 24 times the height 5 gives 24 × 5 = 120, so the volume is 120 cm³.
▸ 120 cm³
Set the length to 6, the width to 4 and the height to 5 and the picture shows volume = 6 × 4 × 5 = 120, with 120 cm³ = 0.12 L in the box below.
Example 2
What is the volume in cm³ of a cube with 5 cm edges, and how many liters is that?
1
Volume of a cube = 5 × 5 × 5 = 125, so it is 125 cm³.
2
Since 1 L = 1000 cm³, 125 cm³ is 125 ÷ 1000 = 0.125 L.
▸ 125 cm³ = 0.125 L
Set the length, width and height all to 5 and the box becomes a cube, with 125 cm³ = 0.125 L shown below.
Unit Review
What is the volume, in liters, of a cube with 10 cm edges?
①1 L
②10 L
③100 L
④0.1 L
▸ ① 1 L
1
Volume = 10 × 10 × 10 = 1000, so it is 1000 cm³.
2
Since 1 L = 1000 cm³, 1000 cm³ is 1 L.
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Prisms and Pyramids

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