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GRADE 6 · MATHEMATICS

Volume of 3D Shapes

Volume tells us how much three-dimensional space an object occupies. Learn to understand volume using unit cubes, calculate the volume of cubes and rectangular prisms, and solve practical measurement problems.

Learning time: approximately 25–30 minutes · Beginner level

What You Will Learn

Explain volume using unit cubes.
Calculate the volume of a rectangular prism.
Use the formula for the volume of a cube.
Choose and write correct cubic units.
Solve everyday volume problems.

1. What Is Volume?

Volume is the amount of space inside a three-dimensional object. Imagine filling a box with small cubes that each measure 1 centimetre on every side. Each cube has a volume of 1 cubic centimetre (1 cm³). Counting how many cubes fit without gaps or overlaps gives the box's volume.

One unit cube

A cube measuring 1 cm × 1 cm × 1 cm has a volume of 1 cm³.

2. Volume of a Rectangular Prism

A rectangular prism (also called a cuboid) has a length, width and height. Its volume is found by multiplying these three measurements.

Volume = length × width × height

V = l × w × h

Worked example

A storage box is 5 cm long, 3 cm wide and 2 cm high. Find its volume.

Write the formula: V = l × w × h.
Substitute the measurements: V = 5 × 3 × 2.
Multiply: V = 30.
Use cubic units: V = 30 cm³.

Answer: 30 cubic centimetres.

3. Volume of a Cube

A cube has six equal square faces, and all its edges have the same length. So its length, width and height are equal.

Volume = side × side × side

V = s³

Worked example

A cube has sides of 4 cm. Find its volume.

V = 4 × 4 × 4 = 64 cm³.

Answer: 64 cubic centimetres.

4. Units of Volume

Volume is measured in cubic units because it measures three dimensions.

Unit	Meaning	Typical use
mm³	Cubic millimetres	Very small spaces
cm³	Cubic centimetres	Small boxes and objects
m³	Cubic metres	Large rooms and containers

Do not confuse area and volume. Area uses square units such as cm². Volume uses cubic units such as cm³. A correct numerical calculation with the wrong unit is not a complete answer.

5. Solve Real-Life Problems

Example 1: A fish tank

A rectangular fish tank is 40 cm long, 20 cm wide and 25 cm high. What is its volume?

V = 40 × 20 × 25 = 20,000 cm³. This is the tank's internal volume if the measurements describe its inside dimensions.

Example 2: A cube-shaped gift box

A cube-shaped gift box has an edge of 6 cm. Its volume is 6 × 6 × 6 = 216 cm³.

Example 3: Find a missing height

A box has a volume of 60 cm³, a length of 5 cm and a width of 4 cm. Its height is 60 ÷ (5 × 4) = 60 ÷ 20 = 3 cm.

6. Common Mistakes

Using only two dimensions: length × width gives the area of the base, not the volume. Multiply by height as well.

Writing square units: Volume needs cubic units, such as cm³, not cm².

Mixing units: Convert measurements to the same unit before multiplying.

Confusing a cube and a cuboid: For a cube, all three dimensions are equal. For a rectangular prism, they may be different.

7. Practice Exercises

Find the volume of a box measuring 7 cm × 2 cm × 3 cm.
Find the volume of a cube with side length 5 cm.
A prism is 8 m long, 2 m wide and 3 m high. Find its volume.
A box has volume 72 cm³, length 6 cm and width 4 cm. Find its height.
Explain why volume is written in cubic units.

Show practice answers

7 × 2 × 3 = 42 cm³.
5 × 5 × 5 = 125 cm³.
8 × 2 × 3 = 48 m³.
72 ÷ (6 × 4) = 3 cm.
Because volume measures three dimensions: length, width and height.

9. Free Printable Worksheet

Print this worksheet or save it as a PDF.

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