Volume of a prism

Volume of a cuboid diagram, with one end of the cuboid shaded in green

We've learned that the volume of a cuboid is its length multiplied by its width multiplied by its height (\(l \times w \times h\)).

The area of the green shaded end of the cuboid (the cross section) is \(w \times h\), so you can also say that the volume of a cuboid is: \(Volume = area~of~cross~section \times length\)

Different types of prism

This formula works for all prisms:

3 different types of prisms
  1. \[\text{volume~of~a~cylinder}=\text{area~of~circle}\times\text{length}\]
  2. \[\text{volume~of~triangular~prism}=\text{area~of~triangle}\times\text{length}\]
  3. \[\text{volume~of~L-shaped~prism}=\text{area~of~L-shape}\times\text{length}\]
Question

a) What is the volume of this triangular prism?

Volume of a triangular prism

b) What is the volume of this prism?

Volume of a triangular prism

a) \(volume = area~of~triangle \times length\)

\[=(\frac{1}{2}\times{2~cm}\times{5~cm})\times{4~cm}\]

\[= \text{20 cm}^3\]

b) The area of the cross section is \(\text{5 cm}^2\) and the length is \(\text{8 cm}\), so the volume is \({5~cm}^{2}\times{8~cm}={40~cm}^{3}\).

Remember that the volume is:

\[the~area~of~the~cross~section\times the~length\]

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