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Find the area of the largest circle which can be cut from a square of edge 4 in. What is the area of the material wasted?
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 |
Area of a square:
The edge of a square is equal to the diameter of a circle as shown in the figure above. A circle is tangent to the sides of a square. If the edge of a square is 4 in., then it follows that the diameter of a circle is 4 in. If the diameter of a circle is 4 in., then the radius of a circle is 2 in.
Area of a circle:
Therefore, the area of material wasted is
