What is the maximum number of 3-cm cubes that can be put into a large box which measures 22 cm x 15 cm x 14 cm?

To find out the maximum number of 3-cm cubes that can fit into a larger box, you need to find the volume of both the larger box and the smaller cubes, then divide the volume of the larger box by the volume of the smaller cube.

Step 1: Find the volume of the larger box. The volume of a box (or a rectangular prism) is found by multiplying its length, width, and height. So, for a box that measures 22 cm x 15 cm x 14 cm, the volume would be:

22 cm * 15 cm * 14 cm = 4,620 cubic cm

Step 2: Find the volume of the smaller cube. The volume of a cube is found by cubing one of its sides. So, for a cube that measures 3 cm on each side, the volume would be:

3 cm * 3 cm * 3 cm = 27 cubic cm

Step 3: Divide the volume of the larger box by the volume of the smaller cube. This will give you the maximum number of smaller cubes that can fit into the larger box.

4,620 cubic cm / 27 cubic cm = 171.11

Since you can't have a fraction of a cube, you would round down to the nearest whole number. So, the maximum number of 3-cm cubes that can fit into the larger box is 171.