Volume of prisms

Objective. Find prism volume using cross-sectional area.

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2. Worked example
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Learn: the key idea

The volume of a prism is found by multiplying the area of its constant cross-section by its length, since a prism is essentially that cross-section repeated along its length. First calculate the area of the 2D cross-sectional shape, such as a triangle or trapezium, then multiply by the prism's length. For a triangular prism with cross-sectional area 12 cm² and length 9 cm, the volume is 12 × 9 = 108 cm³. Always identify the cross-section correctly, as it's the shape that stays the same all along the prism.

Worked example

A triangular prism has a cross-sectional area of 15 cm² and a length of 10 cm. Find its volume.

1 $Recall the formula: volume = cross-sectional area \times length$
2 $Substitute the values: 15 \times 10$
3 $Multiply: 15 \times 10 = 150$
4 $The volume is 150 cm³$

Answer: 150 cm³

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Common mistake. Pupils sometimes multiply all three dimensions together as if the solid were a cuboid, ignoring that the cross-section is a triangle rather than a rectangle. Always calculate the correct cross-sectional area first before multiplying by length.

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