Finding a dimension from the volume

This is the part of Volume that is new at P6: you are given the volume and asked for an edge. The method is always the same — divide the volume by everything you already know. Given two edges, multiply them first and divide by that product. Given the **base area**, divide by it straight away, because the base area already stands for `length × width` and you never need the two edges separately. A cube is the special case: with only one number to find, you look for the edge that gives the volume when it is multiplied by itself three times, and you find it by trying — there is no cube-root key on a PSLE paper.

Worked example

Problem A cuboid has a volume of 480 cm³. Its length is 12 cm and its width is 8 cm. Find its height. A cube has a volume of 512 cm³ — find one of its edges.

volume = length × width × height, so height = volume ÷ (length × width).
Multiply the two edges you are given: 12 × 8 = 96 cm² — the base area again.
Divide: 480 ÷ 96 = 5 cm.
For the cube, try numbers: 7 × 7 × 7 = 343 — too small. 8 × 8 × 8 = 512, so each edge is 8 cm.
Watch out Divide by BOTH known edges. Dividing 480 cm³ by only 12 leaves 40 cm², which is an area — a length can never come from dividing by one number here.
Tip Learn 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125 and 10³ = 1000. Between them they make almost every P6 cube-root question a one-line answer.
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