Obtain two cardboard boxes that are the same size and measure their dimensions. That is, measure their width, length and height.
Calculate the volumes of the cardboard boxes. To obtain the volume of one box, multiply the width, length and height together. The result will be the volume. For example, if the width was two feet, the length was two feet and the length was two feet, the box would have a volume of 2 x 2 x 2, or eight cubic feet. Since both boxes are the same size, that is they have the same dimensions, they will have the same volume.
Calculate the total volume of the cardboard boxes. The volume of the two card boxes is the sum of their individual volumes. If both boxes have a volume of eight cubic feet, the total volume would be 16 cubic feet, that is 8 + 8.
Slide the open face of the boxes slowly into each other, about half the distance of the length of the box and calculate the volume of the newly formed box. Slide the boxes such that each end of each box is only half exposed. Next measure the dimensions of this newly formed box. If you did it right, and the boxes you used has a length of two feet, a width of two feet and a height of two feet, the length of the newly formed box will measure about three feet. The width and height will still be the same, that is two feet and two feet.
Now calculate the volume of the newly formed box. Since the new length is 3 feet, and the height is 2 feet and the width is 2 feet, the new volume would be 3 times 2 times 2 or 12 cubic feet.
Note that the newly merged box has a different form then the two original card board boxes. Its volume is also different. Its volume is greater than each of the original boxes, but less than the sum of the volumes of the two original boxes.
Calculate the overlapping volume. Measure the overlapping length. Since you inserted the box, halfway in, and used a 2 x 2 x 2 box, you should measure an overlap of one foot. The width and height dimensions of the overlapping boxes, however, will still be the same. The volume of the overlapping volume is then 1 x 2 x 2, or four cubic feet, which is the length of the overlap times the width times the height of the box.