Formula sheet
Volume of prism
Area of cross section × height is given on the exam formula sheet. You must still find the correct cross-section area yourself (triangle, trapezium, etc.)
and identify which measurement is the length the prism runs along.
What the symbols mean
- A Area of the uniform cross section, the shape that stays the same along the prism (area unit).
- h Length/height of the prism, the distance the cross section is pushed through (length unit).
Given in the exam, or memorise?
Area of cross section × height is given on the exam formula sheet. You must still find the correct cross-section area yourself (triangle, trapezium, etc.)
and identify which measurement is the length the prism runs along.
Why it works
A prism is a cross section stacked along its length.
- The prism has the same cross section all the way through, area A.
- Imagine stacking thin slices of that shape, each of area A, along a length h.
- The total volume is area × length = A × h.
Worked example 1
A triangular prism has a cross section that is a triangle of base 6 cm and height 4 cm. The prism is 10 cm long.
Find its volume.
- Cross-section area A = ½ × 6 × 4 = 12
- Volume = A × h
- = 12 × 10
- = 120
Worked example 2
A prism has volume 240 cm³ and a cross-section area of 30 cm². Find its length.
- Volume = A × h
- 240 = 30 × h
- h = 240 ÷ 30
- h = 8
Where students go wrong
- Using a random face area instead of the uniform cross section that runs through the prism.
- Mixing up which measurement is the length h and which belongs to the cross section.
- Computing the cross-section area wrongly (e.g. forgetting the ½ for a triangle).
- Giving the answer in cm² instead of cm³.
Use it with
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
What exactly is the cross section of a prism?
It is the flat shape you would see if you sliced the prism straight across, at right angles to its length. In a prism this shape is the same at every slice, that uniform face is the cross section.
Find its area first, then multiply by the length. The moving face, not a side panel, is what counts.
Does this work for a cylinder too?
In spirit yes, a cylinder is like a prism with a circular cross section, so volume = circle area × height = πr² × h. The prism formula and the cylinder formula share the same idea of cross-section area times length.
The formula sheet lists the cylinder separately as πr²h, which is just this rule applied to a circle.
Which length do I multiply by?
Multiply the cross-section area by the length that the shape is pushed through, the distance between the two identical ends. For a triangular prism lying on its side, that is often the horizontal length, not the triangle's own height.
Identify the two matching end-faces first; the gap between them is the length h.