__Category__: Plane Geometry"Published in Vacaville, California, USA"

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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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

or