In a box measuring 40 * 40 * 50, you need to put the same cubes so that it is completely filled.

In a box measuring 40 * 40 * 50, you need to put the same cubes so that it is completely filled. What is the minimum number of cubes needed to fill a box completely? 80 pcs, 200 pcs, or 800 pcs?

T. to. no empty space should remain in this box, the edge of the cube should be equal to the difference between the length of unequal dimensions of the box, i.e. 50 – 40 = 10 cm.

Now let’s calculate the volume of the box and the volume of one cube with a side of 10 cm, respectively:

V cor. = 40 * 40 * 50 = 80,000 (cm 3);
V cub. = 10 * 10 * 10 = 1000 (cm 3).

To find out how many of these cubes will fit in a box, we divide its volume by the volume of one cube:

V cor: V cube = 80000: 1000 = 80 (pieces).

Answer: at least 80 cubes.