Illuminations: Cubes

# 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?

### Instructions

 Along the left side, click on a cube, a row of cubes, or a layer of cubes to fill the box. The Remove Last button takes away the last piece you placed in the box; the Clear button removes all of the pieces from the box. By clicking on the flattened sides of the box, you can see what the box looks like when the sides are folded up. Change the width, depth, and height to see boxes of various sizes.

### Exploration

 The volume of a box is equal to the number of unit cubes that will fit inside it. How many unit cubes are needed to fill a box that measures 3 × 5 × 7? What about a box that measures 5 × 7 × 3? What is the volume 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?

### Lessons

 More and Better Mathematics for All Students
 © 2000 National Council of Teachers of Mathematics Use of this Web site constitutes acceptance of the Terms of Use The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring mathematics learning of the highest quality for all students. The views expressed or implied, unless otherwise noted, should not be interpreted as official positions of the Council.