"Published in Newark, California, USA"
Find the amount of waste in making the largest possible cylindrical rod from a bar of iron 3 ft. long which has a square cross section whose diagonal is 6 in.
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| Photo by Math Principles in Everyday Life |
Solution:
To analyze the given word problem, let's label further the given figure as follows
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| Photo by Math Principles in Everyday Life |
The first that we need to do is to solve for the area of the cross section of the waste material. The cross section of the waste material is the difference of a square and a circle.
By using Pythagorean Theorem, the length of one side of a square which is also the diameter of a circle is
Hence, the area of the cross section of the waste material is
Therefore, the amount of waste material removed from a bar of iron which is the difference of the volume of a square prism and a right circular cylinder is
