A circular piece of metal of maximum size is cut out of a square piece and then a square piece of maximum size is cut out of the circular piece. The total amount of metal wasted is

# A circular piece of metal of maximum size is cut out of a square piece and then a square piece of maximum size is cut out of the circular piece. The total amount of metal wasted is

1. A
$\frac{1}{5}$the area of original square
2. B
$\frac{1}{2}$the area of original square
3. C
$\frac{1}{2}$the area of the circular piece
4. D
$\frac{1}{4}$the area of circular piece

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### Solution:

Let the side of original square be a
Now, radius of circle = $\frac{a}{2}$
Now, the new square is made by joining the midpoints of the original square.
Now, side of new square √{(a/2)2+(a/2)2
=√($\frac{a2}{4}$+$\frac{a2}{4}$)
=√a2/2
= a/√2
Area of wasted metal = area of original square- area of new square
=a2-($\frac{a}{\surd 2}$)2
=a2 -         =$\frac{a2}{2}$
=$\frac{1}{2}$  of the area of the original square.

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