The volume (in m3) of a cube, each of whose edges is 19 m, is:

Concept

A cube is a solid in which the length, the breadth and the height are all the same. If each edge measures a units, its volume is the product of those three equal dimensions: V = a × a × a = a3.

Because three lengths are multiplied together, the result is always expressed in cubic units — cubic metres (m3) when the edge is given in metres.

Application

1. Edge of the cube: a = 19 m.

2. Volume rule: V = a3 = 19 × 19 × 19.

3. Multiply the first two edges: 19 × 19 = 361.

4. Multiply that by the third edge: 361 × 19 = 361 × 20 − 361 = 7220 − 361 = 6859.

5. Therefore V = 6859 m3.

Cross-check

Bracket the result with the nearest whole-number cubes. Since 183 = 5832 and 203 = 8000, the volume of a cube of edge 19 m must lie between 5832 m3 and 8000 m3, which 6859 m3 does. Reversing the last step, 6859 ÷ 19 = 361 = 192, so the multiplication is sound.

A second, faster filter is the units digit. The edge 19 ends in 9, and 9 × 9 × 9 = 729 ends in 9, so the cube of any number ending in 9 must itself end in 9 — which pins the units digit of the volume to 9.

Result

The cube of edge 19 m encloses a volume of 6859 m3.