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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

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\frac{1}{5}

the area of original square

\frac{1}{2}

the area of original square

\frac{1}{2}

the area of the circular piece

\frac{1}{4}

the area of circular piece

answer is B.

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Detailed 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.
So, shaded part is wasted
Now, side of new square √{(a/2)2+(a/2)2
=√(

\frac{a 2}{4}

\frac{a 2}{4}

)
     =√a2/2
     = a/√2
Area of wasted metal = area of original square- area of new square
    =a2-(

\frac{a}{\sqrt 2}

)2
=a2 -

\frac{a 2}{2}

\frac{a 2}{2}

\frac{1}{2}

of the area of the original square.

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