Cubes and Cube Roots

14³ can be read as “14 to the power of 3”, but usually it is read as “14 cubed” because  it represents the volume of a cube with side 14. Volumes of cubes provides a useful geometrical introduction to cubes and cube roots.

Using Materials

Problem: “Norma builds a 4 by 4 by 4 cube layer by layer in linkable cubes. How many cubes does she need?”

Discuss why each layer is 4 by 4 cubes. Discuss how to describe this 4 by 4 by 4 cube in a written form. (Answer: 4 x 4 x 4.)

“What is the alternative way of writing this?” (Answer: 4³.)

Using Imaging

Problem: “Norma builds cubes layer by layer in linkable cubes. Imagine how many cubes she needs for these bigger cubes.” Fold back to building the cubes if needed.

“How many cubes does Norma need to build these larger cubes: 3 by 3 by 3? 2 by 2 by 2? 5 by 5 by 5?”

Using Number Properties

Problem: “An ancient king decides to build a large cubic memorial to his reign from blocks of stone. Each stone is 1 metre by 1 metre by 1 metre.

He plans a memorial that is 89 metres by 89 metres by 89 metres. Use the y^x button on a calculator to find the number of blocks needed.”

(Answer: 89 y^{x 3} 3 = 704 969.)

Examples: Use the y^x button on a calculator to work out
34 x 34 x 34
45 x 45 x 45
0.89 x 0.89 x 0.89
67.2 x 67.2 x 67.2 ...

Problem: “In a chemistry experiment, Lucy grows a blue crystal of copper sulphate that is cubic and that has a volume of 798 cubic millimetres. How long is each edge of  the cube? Round sensibly.”

(Answer: Using the ^x√y button, Lucy enters 798 ^x√y 3 = and the display shows 9.27543523. At best this is 9.3 mm. Note on some calculators, the order is 3 ^x√y