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Question

A circle of maximum possible size is cut from a square sheet of board. Subsequently, a square of maximum possible size is cut from the resultant circle. Area of the final square will be

A
75% of the size of the original square
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B
50% of the size of the original square
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C
75% of the size of the circle
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D
25% of the size of the original square.
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Solution

The correct option is C 50% of the size of the original square
Let the side of the original square be a units. Therefore, the area of the original square =a2 units. The diameter of the circle of maximum possible dimension that is cut from the square will be a units. The diagonal of the square of maximum possible dimension that can be cut from the circle will be a units.
If the diagonal of the final square is a units, then its area a22 units.

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