Volume of a Prism

Statement

The volume of a prism is found by multiplying the area of its cross-section by its length:

\[ V = \text{area of cross-section} \times \text{length} \]

Why it’s true

• A prism is a solid with a uniform cross-section throughout its length.
• If you know the area of that cross-section, multiplying by the length gives the total space inside.

Recipe (how to use it)

1. Identify the cross-section (triangle, rectangle, trapezium, etc.).
2. Calculate its area.
3. Multiply the area by the length of the prism.
4. Give the answer in cubic units.

Spotting it

Prisms are solids where the shape of one end is identical all the way through: cuboids, cylinders, triangular prisms, trapezoidal prisms, etc.

Common pairings

• Often appears with triangular prisms in GCSE exams.
• Can involve compound shapes (cross-section split into rectangles/triangles).

Mini examples

1. Rectangular prism: l=10, w=4, h=3 → area=12, length=10 → V=120.
2. Triangular prism: base=6, height=4 → area=12, length=8 → V=96.

Pitfalls

• Forgetting to calculate the cross-section area first.
• Using slant length instead of perpendicular length.
• Forgetting to cube the units.

Exam strategy

• Sketch the cross-section separately.
• Always label dimensions carefully.
• Leave answers in exact form unless decimals are required.

Summary

The volume of a prism is the area of its cross-section multiplied by its length. Different prisms only differ by the shape of their cross-section.