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

\frac{1}{4}

the area of the original square

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\frac{1}{2}

the area of the original square

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\frac{1}{2}

the area of the circular piece

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\frac{1}{4}

the area of the circular piece

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None of these

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Solution

The correct option is C $\frac{1}{2}$ the area of the original square
Designate a side of the original square by $s$ . Then the radius $r$ of the inscribed circle is $s / 2$ . A side of the second square. (inscribed in the circle) is $r \sqrt{2} = s / \sqrt{2}$ . Therefore, the area of the second square is $s^{2} / 2$ , while the original square is $s^{2} . ∴ (b)$ is the correct choice.

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Question 3

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. What will be the area of the final square?
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Q. A wire of length

28

cm is to be cut into

2

pieces,

1

piece is to be made into a square & the other one into a circle what should be the length of

2

piece so that the combined area of the square & the circle is min?

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