EDEXCEL GCSE FOUNDATION MATHS - What is the Volume of a Sphere or Cone

Edexcel GCSE Foundation Maths: Volume of a Sphere and Cone

What is volume?

Volume is the amount of 3-dimensional space an object takes up. It's measured in cubic units, like cubic centimetres (cm³) or cubic metres (m³).

Volume of a Sphere

A sphere is a perfectly round 3D object.

Formula:

• V = (4/3)?r³

Where:

• V = Volume of the sphere
• ? (pi) ? 3.142
• r = Radius of the sphere

Example:

A sphere has a radius of 5cm. Calculate its volume.

1. Substitute the value of r into the formula: V = (4/3)?(5cm)³
2. Calculate: V ? (4/3) × 3.142 × 125cm³ ? 523.6cm³

Therefore, the volume of the sphere is approximately 523.6 cm³.

Volume of a Cone

A cone is a 3D object with a circular base and a pointed top.

Formula:

• V = (1/3)?r²h

Where:

• V = Volume of the cone
• ? (pi) ? 3.142
• r = Radius of the base of the cone
• h = Height of the cone

Example:

A cone has a radius of 4cm and a height of 6cm. Calculate its volume.

1. Substitute the values of r and h into the formula: V = (1/3)?(4cm)²(6cm)
2. Calculate: V ? (1/3) × 3.142 × 16cm² × 6cm ? 100.5cm³

Therefore, the volume of the cone is approximately 100.5 cm³.

Key points to remember:

• Always remember to use the correct formula for each shape.
• Make sure to include the correct units in your answer.
• Round your answer to an appropriate degree of accuracy, usually to one or two decimal places.
• Practice using these formulas with different examples to solidify your understanding.