What is the maximum number of 3-cm cubes that can be put into a closed box measuring 20 cm by 8 cm by 12 cm?

To find out the maximum number of 3-cm cubes that can be put into a closed box measuring 20 cm by 8 cm by 12 cm, you need to find the volume of both the box and the cube, and then divide the volume of the box by the volume of the cube.

Step 1: Find the volume of the box The volume of a box (or a rectangular prism) can be found by multiplying its length, width, and height. So, the volume of the box is 20 cm * 8 cm * 12 cm = 1920 cubic cm.

Step 2: Find the volume of the cube The volume of a cube can be found by cubing one of its sides. So, the volume of the cube is 3 cm * 3 cm * 3 cm = 27 cubic cm.

Step 3: Divide the volume of the box by the volume of the cube The maximum number of cubes that can fit in the box is the volume of the box divided by the volume of the cube. So, the maximum number of cubes is 1920 cubic cm / 27 cubic cm = approximately 71.11.

However, you can't have a fraction of a cube, so you need to round down to the nearest whole number. Therefore, the maximum number of 3-cm cubes that can be put into the box is 71.