Sheet № 102 · Foundation + Higher · AQA · Edexcel · OCR
Volume of a Prism –
Prism questions are among the most reliable mark-earners at GCSE. The formula is straightforward — area of the cross-section multiplied by the length — but success depends on correctly identifying the cross-section and calculating its area first. This topic appears on both Foundation and Higher papers across AQA, Edexcel and OCR.
§Key definitions
Question:
A triangular prism has a triangular cross-section with base 8 cm and perpendicular height 5 cm. The prism is 12 cm long. Find its volume.
Q1 (Foundation):
A triangular prism has a cross-section with base 6 cm and height 4 cm. The prism is 10 cm long. Find its volume.
Q2 (Foundation):
A cuboid measures 9 cm by 4 cm by 5 cm. Find its volume.
Q3 (Higher):
A prism has a pentagonal cross-section with area 42 cm². The prism is 18 cm long. Find its volume.
§Formulas to memorise
V = area of cross-section × length
For a triangular prism: V = ½ × base × height × length
Cross-section area = ½ × 8 × 5 = 20 cm²
Volume = 20 × 12 = 240
Cross-section area = ½(6 + 10) × 4 = ½ × 16 × 4 = 32 cm²
Volume = 32 × 15 = 480
Full rectangle area = 7 × 5 = 35 cm²
Removed rectangle area = 3 × 2 = 6 cm²
L-shaped cross-section area = 35 − 6 = 29 cm²
Volume = 29 × 20 = 580
Worked example
A triangular prism has a triangular cross-section with base 8 cm and perpendicular height 5 cm. The prism is 12 cm long. Find its volume.
Working: Cross-section area = ½ × 8 × 5 = 20 cm² Volume = 20 × 12 = 240
⚠ Common mistakes
- ✗Confusing the cross-section with a side face. The cross-section is the face that stays the same along the length. It is usually the shape shown "face-on" in the diagram.
- ✗Using the slant side of a triangle instead of the perpendicular height. When the cross-section is a triangle, you need the height at right angles to the base.
- ✗Multiplying by the wrong dimension. After finding the cross-sectional area, multiply by the length that runs perpendicular to the cross-section, not another dimension of the cross-section.
- ✗Forgetting cubic units. Volume is measured in cm³ or m³, not cm² or cm. If your units are wrong, the examiner knows you have confused area and volume.
✦ Exam tips
- →Always write "area of cross-section = ..." as a separate step. This earns a method mark and keeps your working clear.
- →If the cross-section is a compound shape, find its area using addition or subtraction of simpler shapes before multiplying by the length.
- →The prism formula is not on the formula sheet for AQA or Edexcel — you must memorise it.
- →When asked for volume in a real-world context (e.g. filling a container), check if you need to convert units or state capacity in litres (1000 cm³ = 1 litre).