Volume of Prisms – Cross-Section Area × Length
Every prism – no matter what shape its cross-section is – shares the same volume formula: V = (cross-section area) × length. This works because a prism is just its cross-section shape “extruded” along its length, like stamping the same 2D shape repeatedly and stacking the copies up.
This single formula quietly contains the cuboid formula you already know: a cuboid is a rectangular prism, so its volume is (l × w) × h – cross-section area times length – which is exactly the same thing as V = lwh written a different way.
Calculating a Prism's Volume
V = (cross-section area) × length. For a triangular prism, first find the triangle's area, then multiply by the prism's length.
A triangular prism has a triangular cross-section with base 5 cm and height 8 cm, and a length of 15 cm. Find its volume.
Triangle area = ½ × 5 × 8 = 20 cm². V = 20 × 15 = 300 cm³.
Real-Life Application
- Tents: calculating the interior space of a triangular-prism-shaped tent.
- Swimming pools: pools with a sloped bottom form a trapezoidal-prism shape.
- Toblerone bars: calculating the volume of chocolate inside the packaging.
Key Takeaways
- Every prism's volume is (cross-section area) × length.
- This single formula works for any cross-section shape.
- The cuboid volume formula, V = lwh, is a special case of this rule.
Practice: Volume of Prisms
Volume of Prisms
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