How many boxes 120 centimeters long by 25 centimeters wide by 10 centimeters high fit in 1 cubic meter?

Answer 1

A box that has a volume of 1 cubic meter is equal to 1,000,000 cubic centimeters, because 1m x 1m x 1m is equal to 100cm x 100cm x 100cm = 1003cm3 = 1,000,000cm3. (Don't confuse the exponent "3" on the centimeter, it is simply there to denote that we are dealing with volume)

Now that we have the volume of the cube in the proper units, we must find the volume of the boxes in question.

Again, we will multiply the three side length values to get the volume of our box.

120cm x 25cm x 10cm = 30,000cm3

So now we divide 1,000,000cm3 by 30,000cm3 to get 33.33 (repeating).

Now, although this is mathematically correct, it is not practical. This number implies that we will fit a third of a box in the larger cube, and I'm sure it is assumed that you cannot cut the boxes into different shapes or sizes.

In reality, we cannot fit any boxes into the cube (unless they are put in diagonally, but I don't believe that is what is expected). If the box length is 120cm and the cube length (in any axis direction) is only 100cm, we will never be able to fit a box inside this cube without cutting it in some way (or placing it in diagonally as previously stated.

Of course, we don't fully know if the cubic meter is actually a cube, it might be a rectangular prism. In that case, with the information we have, we would say that the cube has dimensions such that the maximum possible number of boxes to fit inside this cube is 33 (we remove the third of a box because we cannot cut any of the boxes).