Lesson 11

Use the 32 snap cubes in the applet’s hidden stack to build the largest single cube you can. Each small cube has side length of 1 unit.

1. How many snap cubes did you use?
2. What is the side length of the cube you built?
3. What is the area of each face of the built cube? Show your reasoning.
4. What is the volume of the built cube? Show your reasoning.

Make sure to include correct units of measure as part of each answer.

1. A square has side length 10 cm. Use an exponent to express its area.
2. The area of a square is $7^2$ sq in. What is its side length?
3. The area of a square is 81 m². Use an exponent to express this area.
4. A cube has edge length 5 in. Use an exponent to express its volume.
5. The volume of a cube is $6^3$ cm³. What is its edge length?
6. A cube has edge length $s$ units. Use an exponent to write an expression for its volume.

When we multiply two of the same numbers together, such as $5\boldcdot 5$, we say we are squaring the number. We can write it like this: $\displaystyle 5^2$

Because $5\boldcdot 5 = 25$, we write $5^2 = 25$ and we say, “5 squared is 25.”

When we multiply three of the same numbers together, such as $4\boldcdot 4 \boldcdot 4$, we say we are cubing the number. We can write it like this: $\displaystyle 4^3$

Because $4\boldcdot 4\boldcdot 4 = 64$, we write $4^3 = 64$ and we say, “4 cubed is 64.”

We also use this notation for square and cubic units.

• A square with side length 5 inches has area 25 in².
• A cube with edge length 4 cm has volume 64 cm³.

To read 25 in², we say “25 square inches,” just like before.

The area of a square with side length 7 kilometers is $7^2$ km². The volume of a cube with edge length 2 millimeters is $2^3$ mm³.

In general, the area of a square with side length $s$ is $s^2$, and the volume of a cube with edge length $s$ is $s^3$.