Required Mathematical Intelligence

Chapter 75
The rough carpenter brought a small wooden pillar carved with patterns and said:
"Once a scholar living in London brought me a log three feet long, one foot wide and one foot thick, and asked me to hew it and carve it into a post, as you see now. The scholar promised to compensate me for the wood I cut in my work. I first weighed the square log, and it weighed exactly 3 pounds, while the post to be made only weighed 1 pounds. Therefore, I weighed the square log from the square log. 30 cubic foot of wood was cut, which is one-third of the original. But the scholar denies it, saying that the volume cut cannot be calculated by weight, because the middle part of the square is said to be heavier, and it may be the other way around Pray, how do I prove in this case to a fastidious scholar how much wood was cut?"

At first glance, this question appears difficult, but the answer is so simple that the rough carpenter's method is well known.This kind of cleverness is also very useful in daily life.

[Answer: The carpenter said that he made a box with the exact same internal dimensions as the original square wood, that is, 3×1×1. Then, he put the carved wooden pillars into the box, and in the gap Filled with dry sand.Then, he vibrated the box carefully so that the sand in the box was filled and flush with the mouth of the box.Then the carpenter took out the post gently, without bringing out any grain of sand, and leveled the sand in the box. The depth was measured, and it was proved that the space occupied by the post was exactly 2 cubic feet.That is, the carpenter cuts away one cubic foot of lumber. ]
(End of this chapter)