A prism has the same cross-sectional shape running all the way through it. Whatever that cross-section's area ($A$) is, the volume is simply that area multiplied by the prism's length:

This formula is given on the exam formula sheet — so the real skill being tested isn't memorising it, but correctly working out $A$, the area of whatever 2D shape the cross-section happens to be.

For a cuboid, the cross-section is a rectangle, so $A = l\times w$, giving the familiar $V=lwh$ (this one is expected to be memorised, unlike the general prism formula). For a triangular prism, $A=\frac12 \times \text{base} \times \text{height}$ of the triangle — forgetting the $\frac12$ here is a very common error, and it doubles your final volume.

A cylinder is a circular prism, so $A=\pi r^2$, giving:

1. Find any missing side lengths by subtracting known dimensions from the overall length/width.
2. Split the cross-section into simple rectangles.
3. Add the areas of the rectangles together to get the total cross-sectional area $A$.
4. Multiply by the prism's length as usual: $V=A\times l$.

Since the whole answer depends on first getting the 2D decomposition right, a mistake in step 1 or 2 guarantees an incorrect volume — treat the area calculation as the real test here, not the final multiplication.

If the cross-sectional area is already given as, say, $18\text{ cm}^2$, do not square it again — it's already an area, not a length.

Capacity: $1\text{ cm}^3 = 1\text{ mL}$, and $1000\text{ cm}^3=1\text{ L}$.

Density: mass = density × volume ($M = D\times V$). Watch for unit mismatches — if density is given in $\text{g/cm}^3$ but a dimension is in metres, convert using the cubic factor, $1\text{ m}^3=1{,}000{,}000\text{ cm}^3$, not the linear ×100.

A triangular prism has a cross-section that is a right-angled triangle with legs 6 cm and 8 cm, and the prism is 15 cm long. Find its volume.

1. Cross-sectional area: $A = \frac12 \times 6 \times 8 = 24\text{ cm}^2$.
2. Volume: $V = A \times l = 24 \times 15 = 360\text{ cm}^3$.