a circle of maximum possible size is cut from a square sheet of board .subsequently a square maximum possible size can be cut from the resultant circle what will be the area of the final square
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74
Let a be the side of a square sheet .
2
Then,area of big square sheet=a
Now , we make circle of maximum possible size from it .
Then the radius of a circle = a/2
So,its diameter(d)=2 x a/2 = a
Now,any square in a circle of maximum size will have the length of diagonal equal to the diameter of the circle .
i.e.diagonal of square made inside the circle = a
so the side of this square =a/square root of 2
2
Therefore,Area of this square=a /2
area of final square is 1/2 of original square .
2
Then,area of big square sheet=a
Now , we make circle of maximum possible size from it .
Then the radius of a circle = a/2
So,its diameter(d)=2 x a/2 = a
Now,any square in a circle of maximum size will have the length of diagonal equal to the diameter of the circle .
i.e.diagonal of square made inside the circle = a
so the side of this square =a/square root of 2
2
Therefore,Area of this square=a /2
area of final square is 1/2 of original square .
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18
Answer:
From the figure :
Area of final square PQRS is half the area of the square ABCD
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