The idea in brief. The volume divided by the height leaves ONE floor, and a floor is an AREA, not a length. The base is a square, so its two sides are the same number and that number times itself is the area, which is exactly what the square-root sign asks for. A cube is the same sentence one dimension up: three edges the same, so the volume is one number times itself twice, and the cube root gives it back. In the lesson. The edge of a cube is the cube root of its volume.
Lesson video, with the working
Finding a cuboid dimension from its volume
2 min 54 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
How do you solve missing dimension of a cuboid questions in P6?
These questions give the volume and ask for something the volume was built from: a length, a height, the edge of a cube or the area of one face.
What your child learns here
These questions give the volume and ask for something the volume was built from: a length, a height, the edge of a cube or the area of one face. This is the heart of the Primary 6 Volume of Cube and Cuboid outcomes, which all run the volume rule backwards.
Find one dimension of a cuboid by dividing its volume by the other two dimensions.
Find the height by dividing the volume by the base area.
Find the edge of a cube as the cube root of its volume.
Find the area of a face by dividing the volume by the one remaining dimension, or by squaring a cube's edge.
Use the square root and cube root signs, and convert litres to cubic centimetres first when needed.
Does the answer make sense?
Each answer is a length in cm or an area in square centimetres, never cubic units. A cube's edge is far smaller than its volume: for a volume in the hundreds your child should expect a one-digit edge, and for a volume in the thousands an edge between 10 and 22.
How to practise these questions
Basic questions train finding the edge of a cube from its volume, and the side of a square from its area. Intermediate questions add a unit conversion first, and answers that must be an area rather than a length. Challenge questions use larger cubes, or two unknown base edges linked by a relation. If working back from a volume stalls, read the written step-by-step solution.
Questions parents ask
How do you find the height of a cuboid from its volume? Divide the volume by the base area. If the base area is not given, multiply the length by the breadth first.
How do you find the edge of a cube from its volume? Find the number that multiplied by itself three times gives the volume. This is the cube root, and the Primary 6 syllabus includes using the cube root sign for it.
What does the P6 syllabus say about volume? It lists finding one dimension of a cuboid from its volume and the other dimensions, the edge of a cube from its volume, the height from the volume and base area, and the area of a face from the volume and one dimension. Using the square root and cube root signs is part of it too.
