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

75 %

of the size of the original square

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50 %

of the size of the original square

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75 %

of the size of the circle

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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 $= a^{2}$ 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 $\frac{a^{2}}{2}$ units.

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