## Cubes

Fill a box with cubes, rows of cubes, or layers of cubes. The number of unit cubes needed to fill the entire box is known as the *volume* of the box. Can you determine a rule for finding the volume of a box if you know its width, depth, and height?

**This interactive is optimized for your desktop and tablet.**

### Objective

- Find the surface area and volume of each box.
- By clicking on the flattened sides of the box, you can see what the box looks like when the sides are folded up.

### How to Use

- Along the left side, click on a cube, a row of cubes, or a layer of cubes to fill the box.
- The
**Undo**button takes away the last piece you placed in the box; the**Clear**button removes all of the pieces from the box. - Use the
**Customize**wheel to change the width, depth, and height to see boxes of various sizes. 20 is the maximum width, depth, and height. - You can also randomize the dimensions by clicking on the
**Next**arrow.

Consider the following questions:

- How many unit cubes are needed to fill a box that measures 3 × 5 × 7?
- How many squares are needed to cover that box?
- What about the volume and surface area of a box that measures 5 × 7 × 3?
- What is the volume and surface area of a box that measures 7 × 3 × 5?

In general, how can you find the volume of a box if you know the width, depth, and height?

How about its surface area?