Grade 5 Volume: Counting Unit Cubes

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   A box is packed with unit cubes. The bottom layer has 3 rows of 3 cubes, and there are 4 layers. How many unit cubes fill the box?

   1. Count the bottom layer: 3 rows of 3 cubes is 3 × 3 = 9 cubes.
   2. There are 4 layers like it: 9 × 4 = 36.
   3. 36 unit cubes fill the box.

   Answer: 36

2. Example 2

   A box holds 16 unit cubes in all. Each layer has 4 cubes. How many layers of cubes are in the box?

   1. Layers × cubes in each layer = all the cubes, so divide: 16 ÷ 4.
   2. 16 ÷ 4 = 4. Check: 4 × 4 = 16.
   3. There are 4 layers of cubes in the box.

   Answer: 4

3. Example 3

   A big cube is built from unit cubes, with 5 cubes along each edge. How many unit cubes does it take?

   1. One layer is 5 × 5 = 25 cubes.
   2. A cube is as tall as it is wide: 5 layers. 25 × 5 = 125.
   3. It takes 125 unit cubes.

   Answer: 125