Surface Area and Volume of Prisms
KS3, GCSE and IGCSE geometry support for prisms and compound solids.
Measuring solids with a constant cross-section
A prism has the same cross-section throughout its length. Students use area knowledge to calculate its volume and analyse every face to calculate surface area. This KS3, GCSE and IGCSE topic is part of wider Geometry Lessons and measures work.
Key formulae and method
Volume of a prism = area of cross-section × length. Surface area is the sum of the areas of all external faces. Begin by identifying the cross-section, label dimensions, calculate its area, then multiply by the prism length. For surface area, use a net or systematic face list so no rectangle or end face is missed.
Worked examples
Example 1: A rectangular prism is 8 cm by 5 cm by 3 cm. Volume = 8 × 5 × 3 = 120 cm³. Example 2: A triangular cross-section has base 6 cm and height 4 cm. Its area is 12 cm². With prism length 10 cm, volume = 120 cm³. Example 3: A cuboid 4 cm by 3 cm by 2 cm has surface area 2(12 + 8 + 6) = 52 cm².
Common mistakes and exam advice
Do not confuse square and cubic units, forget the one-half in a triangular area, or use the sloping edge as a perpendicular height. Surface area requires every exposed face, while volume uses the cross-sectional area only once. Pythagoras’ Theorem may be needed to find a missing sloping length.
Practice exercises and answers
Exercise 1: A cuboid is 7 cm by 4 cm by 3 cm. Answer: volume = 84 cm³. Exercise 2: A triangular prism has cross-section base 8 cm, height 5 cm and length 12 cm. Answer: cross-sectional area = 20 cm²; volume = 240 cm³. Exercise 3: A cube has side 6 cm. Answer: surface area = 6 × 36 = 216 cm².
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