Volume · Grade 9

In Grade 9 you learn: cones, pyramids and spheres.

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

  • 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

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 2

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

Answer: 120 cm³

Example 3

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

Answer: 120 cm³

Example 4

A cylinder has radius 3 cm and height 10 cm. Find its volume, to 1 d.p.

Answer: 282.7 cm³

Example 5

A cylinder has a volume of 90π cm³ and a radius of 3 cm. Find its height.

Answer: 10 cm

Example 6

Find the volume of a sphere with radius 3 cm, to 1 decimal place.

Answer: 113.1 cm³

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