"Published in Newark, California, USA"
A log with a circular cross section is 15 ft. long and 27 in. in diameter at the smaller end. Find the dimensions of the largest piece of timber of length 15 ft. with a uniform square cross section , that can be cut from the log.
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
In this problem, we will cut the log in order to get the largest piece of timber of the same length which is 15 ft. and the cross section is a square. Now, let's consider the cross section of a log after it is cut as follows
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| Photo by Math Principles in Everyday Life |
The diameter of a log is the hypotenuse of a cross section which is a square that passes through its center. By Pythagorean Theorem, the length of the sides of a square is
Therefore, the dimensions of a largest timber that can be cut from the log is
