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Find the volume and total area of the largest cube of wood that can be cut from a log of circular cross section whose radius is 12.7 in.
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| Photo by Math Principles in Everyday Life |
Solution:
Since the radius of a wood log is given, we have to consider the cross section of a wood log as follows
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| Photo by Math Principles in Everyday Life |
As you notice that a square is inscribed in a circle. There are 6 equal squares in a cube and so all the sides of a cube are equal. The radius of a wood log or a circle is equal to ½ of its diagonal. The diagonals of a square bisect each other at a right angle. A right triangle that has two equal sides and two equal angles is called an isosceles right triangle. In this figure, there are four isosceles right triangles in a square. By Pythagorean Theorem,
The length of a side of a cube is 17.9605 in.
The total area of a cube is
The volume of a cube is
