Volume · Grade 8

In Grade 8 you learn: volume of prisms and cylinders.

Volume is how much space a solid takes up, measured in cubic units such as cm³ and m³. Count the cubes, or multiply: for a rectangular prism, length × width × height; for any prism or cylinder, the area of the cross-section × the length.

Key facts

Volume is measured in cubic units: count the 1 cm cubes that fill a solid.
Rectangular prism: V = length × width × height.
Any prism: V = area of cross-section × length.
Cylinder: V = πr²h.
1 litre = 1,000 cm³, and 1 cm³ holds 1 ml.

Worked examples

Example 1

Find the volume of a cube with edges of 4 cm.

Answer: 64 cm³

Example 2

A rectangular prism is 5 cm long, 3 cm wide and 2 cm high. Find its volume.

Answer: 30 cm³

Example 3

A box is filled with 1 cm cubes: 5 along, 3 deep and 2 layers high. How many cubes fill it, and what is its volume?

Answer: 30 cubes, 30 cm³

Example 4

A fish tank is 60 cm long, 30 cm wide and 40 cm tall. A tap fills it at 6 litres per minute. How long does it take to fill?

Answer: 12 minutes

Example 5

A rectangular prism has a volume of 60 cm³. It is 5 cm long and 4 cm wide. How tall is it?

Answer: 3 cm

Example 6

A prism has a cross-section with an area of 15 cm² and is 8 cm long. Find its volume.

Answer: 120 cm³

Example 7

A triangular prism is 10 cm long. Its end is a triangle with base 6 cm and height 4 cm. Find its volume.