The volume of a rectangular prism is how much space it takes up, measured in cubic units. The formula is short, but the questions that trip students up are the ones that run it backwards, so this page covers both directions.
V = l × w × h
Volume equals length times width times height. Another way to see it is base area times height, since length times width is the area of the base. That second reading matters, because it is the version that generalises to prisms whose base is not a rectangle.
A box measures 8 cm long, 5 cm wide and 3 cm high. Find its volume.
Answer: 120 cm³
A tank has a volume of 240 cm³. Its base measures 8 cm by 5 cm. How tall is it?
Answer: 6 cm
A crate is 1.2 m long, 80 cm wide and 50 cm high. Find its volume in cubic metres.
Answer: 0.48 m³
Work through these in order. Each answer opens to show the full method, so you can check your reasoning rather than just your final number.
Find the volume of a prism 2 cm × 3 cm × 4 cm.
Answer: 24 cm³
V = 2 × 3 × 4 = 24 cubic centimetres.
Find the volume of a cube with edge 5 cm.
Answer: 125 cm³
All edges are equal, so V = 5 × 5 × 5 = 125 cm³.
A box is 10 cm × 4 cm × 2 cm. What is its volume?
Answer: 80 cm³
V = 10 × 4 × 2 = 80 cm³.
A prism has base area 12 cm² and height 5 cm. Find its volume.
Answer: 60 cm³
V = base area × height = 12 × 5 = 60 cm³.
A prism 6 cm × 4 cm × h has volume 96 cm³. Find h.
Answer: 4 cm
Base area is 6 × 4 = 24, so 96 = 24h and h = 96 ÷ 24 = 4 cm.
A fish tank is 60 cm × 30 cm × 40 cm. How many litres does it hold? (1000 cm³ = 1 litre)
Answer: 72 litres
V = 60 × 30 × 40 = 72,000 cm³, and 72,000 ÷ 1000 = 72 litres.
A cube has volume 216 cm³. Find the length of one edge.
Answer: 6 cm
The edge is the cube root of 216. Since 6 × 6 × 6 = 216, the edge is 6 cm.
A prism has volume 180 cm³, length 9 cm and height 4 cm. Find its width.
Answer: 5 cm
180 = 9 × w × 4 = 36w, so w = 180 ÷ 36 = 5 cm.
Each edge of a cube is doubled. By what factor does the volume increase?
Answer: 8 times
Volume depends on three dimensions, so doubling each multiplies the volume by 2 × 2 × 2 = 8.
A box 20 cm × 15 cm × 10 cm is filled with 1 cm cubes. How many fit?
Answer: 3000 cubes
The volume is 20 × 15 × 10 = 3000 cm³, and each cube occupies 1 cm³, so 3000 cubes fit.
Generate a rectangular prism volume test at the grade and difficulty you need, with a complete worked answer key and equivalent versions for retakes.
Prefer free practice first? free geometry worksheets with answers
Most students first meet volume as length times width times height, which works perfectly for a box and then stops working the moment the base is a triangle or a circle. Reading the same formula as base area times height is the version that survives. A cylinder is πr² times height, a triangular prism is half base times perpendicular height times length, and in every case the structure is identical: find the area of the face that repeats, then multiply by how far it repeats.
Teaching it this way in Grade 5 costs nothing extra and removes an entire relearning step in Grade 8. It also makes the reverse questions obvious, because if volume is base area times height, then height is volume divided by base area without any rearranging to memorise.
Almost every exam question that carries more than one mark runs the formula backwards. You are given a volume and asked for a missing edge, or given a capacity in litres and asked for a depth. The arithmetic is a single division, but students who have only practised forward substitution often do not recognise that a division is what is wanted.
The reliable habit is to write the formula first, substitute everything you know including the unknown as a letter, and only then decide what to do. A student who writes 240 = 40 × h has already solved the hard part; a student who starts by hunting for numbers to multiply usually stalls.
✗ Writing the answer in square units, such as 120 cm².
✓ Volume is three-dimensional, so the units are cubic: 120 cm³.
✗ Multiplying dimensions that are in different units.
✓ Convert every measurement to the same unit before multiplying, then state the matching cubic unit.
✗ Adding the three dimensions instead of multiplying them.
✓ Volume is a product. Adding gives a length, not a volume, and the units alone reveal the error.
✗ Assuming doubling one edge doubles the volume in every case.
✓ Doubling one edge doubles the volume; doubling all three multiplies it by eight.