GCSE MATHS • HIGHER TIER
Volume of Prisms Made Simple
Learn how to identify a prism, find its cross-sectional area, calculate volume, and rearrange the prism formula to find missing measurements.
Clear method
Exam practice
Worked proofs
Three-Figure Bearings in Four Moves
1
Identify
Identify the constant cross-section of the prism.
2
Area
Calculate the area of the cross-section.
3
Multiply
Multiply the cross-sectional area by the prism length.
4
Units
Give the final volume in cubic units such as cm³, m³ or mm³.
What You’ll Learn
Understand volume
Understand that volume measures the amount of space inside a three-dimensional object and is measured in cubic units.
Recognise a prism
Identify a prism as a three-dimensional shape with a constant cross-section throughout its length.
Find the cross-sectional area
Calculate the area of the shape at the end of the prism before finding its volume.
Calculate volume
Use Volume = Cross-sectional Area × Length to calculate the volume of a prism.
Find missing measurements
Rearrange the prism formula to find a missing cross-sectional area or length.
Key Rules
Use the prism formula
Volume = Cross-sectional Area × Length
Find the cross-section first
Calculate the area of the constant end shape before multiplying by the length.
Use the correct area formula
The cross-section may be a rectangle, triangle, trapezium or another shape, so use the appropriate area formula.
Use cubic units
Volume must be written in cubic units such as cm³, m³ or mm³.
Worked Proof: Triangular Prism
Question: A triangular prism has a triangular cross-section with base 6 cm and height 4 cm. The prism length is 10 cm.
1. Identify
The cross-section is a triangle.
2. Find the cross-sectional area
Area = ½ × 6 × 4 = 12 cm²
3. Identify the length
Length = 10 cm
4.Calculate the volume
Volume = 12 × 10 = 120 cm³
5. Answer
Volume = 120 cm³
More Worked Examples
1
Rectangular Prism
Question: A rectangular prism has a cross-sectional area of 12 cm² and a length of 8 cm.
Volume = Area × Length
= 12 × 8
= 96 cm³
= 12 × 8
= 96 cm³
2
Trapezium Cross-Section
Question: A prism has a trapezium cross-section with area 15 cm² and length 9 cm.
Volume = 15 × 9
= 135 cm³
= 135 cm³
3
Finding the Cross-Sectional Area
Question: A prism has volume 200 cm³ and length 10 cm. Find the cross-sectional area.
Area = Volume ÷ Length
= 200 ÷ 10
= 20 cm²
= 200 ÷ 10
= 20 cm²
4
Finding the Length
Question: A prism has volume 360 cm³ and cross-sectional area 30 cm². Find the length.
Length = Volume ÷ Area
= 360 ÷ 30
= 12 cm
= 360 ÷ 30
= 12 cm
- Common GCSE Mistakes
- Cross-section first: Calculate its area before finding volume.
- Area, not perimeter: Use the cross-sectional area.
- Keep units consistent: Do not mix measurement units.
- Cubic units: Write volume in cm³, m³ or mm³.
- Check arithmetic: Recheck multiplication and division.
- Exam Tips
- Identify the cross-section before calculating.
- Write V = A × L before substituting.
- Show the cross-sectional area separately.
- Rearrange carefully for missing values.
- Check that volume answers use cubic units.
Skills Used in Volume of Prisms
Mensuration
Scale Drawings
Similar Shapes
Compound Shapes
Volume of Cylinders
Surface Area
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Volume of Prisms Tutorial
Step-by-step walkthroughs of Volume of Prisms with clear methods and exam tips.
Frequently Asked Questions
Volume = Cross-sectional Area × Length.
The cross-section is the constant shape at the end of the prism and remains the same throughout its length.
Find the area of the triangular cross-section first, then multiply that area by the length of the prism.
Divide the volume by the prism length.
