# Volume of a prism

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:

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?

b) What is the volume of this 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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