Volume of a prism
A prism is a solid with a uniform cross section. This means that no matter where it is sliced along its length, the cross section is the same size and shape (congruent).
A well-known example of a prism is a cylinder and you can see from the image above that the front face (cross section) is the same size of circle no matter where you slice it.
The formula for the volume of a prism where \(A\) is the area of the cross section and \(h\) is the height/length of the solid is:
\(V = Ah\)
Example
This shape is a triangular prism so the area of the cross section is the area of a triangle.
Answer
Area of the triangle:
\(A = \frac{1}{2}bh\)
\(= \frac{1}{2} \times 6 \times 4\)
\(= 12c{m^2}\)
Volume of the prism:
\(V = Ah\)
\(= 12 \times 12\)
\(= 144c{m^3}\)
Question
Calculate the volume of a triangular prism like the one in the example. However instead of the measurements 12cm, 6cm and 4cm use measurements 14cm, 8cm and 5cm respectively.
Area of the triangle
\(A=\frac{1}{2}bh\)
\(=\frac{1}{2}\times 8\times 5\)
\(=20cm^{2}\)
Volume of the prism
\(V=Ah\)
\(=20\times 14\)
\(=280cm^{3}\)
More guides on this topic
- Determine the gradient of a straight line
- Circle geometry
- Applying Pythagoras Theorem
- Applying the properties of shapes to determine an angle
- Using similarity
- Working with two-dimensional vectors
- Working with three-dimensional coordinates
- Using vector components
- Calculating the magnitude of a vector
- An Approximate History of Co-ordinates