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:
- \(\text{volume of a cylinder}=\text{area of circle}\times\text{length}\)
- \(\text{volume of triangular prism}=\text{area of triangle}\times\text{length}\)
- \(\text{volume of L-shaped prism}=\text{area of L-shape}\times\text{length}\)
This object is a triangular prism so the area of the cross-section is the area of a triangle.
Area of the triangle:
\(= \frac{1}{2} \times 6 \times 4\)
\(= 12cm^{2}\)
\(Volume\,of\,prism\,= Area\,of\,cross-section\times height\,of\,prism\)
\(= 12 \times 13\)
\(= 156cm^{3}\)
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:
\(the~area~of~the~cross~section\times the~length\)
