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October 16th, 2011, 02:41 AM   #1
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Punching Machine

A punching machine is used to create a circular diameter 2 unit from a square sheet of aluminium of width 2 unit. The hole is punched such that the circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with the diagonal of the square.The area of the sheet that remains after punching is...???

a)10/7 square unit
b)22/7 square unit
c)5/7 square unit
d)9/7 square unit
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October 16th, 2011, 06:04 AM   #2
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Re: Punching Machine

Set up a coordinate system with origin at the center of the circle cut out and x and y axes parallel to the edges of the metal sheet. Then the circle has equation . The point P, since it lies on the circle, along the diameter y= -x, is at and the edges of the metal sheet are given by and . Those edges cut the circle again at and . The line from the origin to is, of course, y= x so the lines from the origin to P and that point form a 90 degree angle. That means that the triangle formed by those two lines and the top edge of the metal sheet has area (1/2)(2)(2)= 2 square units. If we were able to go out to the circle itself, that would be 1/4 the area of the entire circle, . So the area that has been cut off the circle by going outside the metal sheet, on that side, is and, since the the other side is symmetrical, the whole area punched out is . Since the metal sheet has area 4 square units, there will be square units left.
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October 16th, 2011, 06:45 AM   #3
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Re: Punching Machine

Hi HallsOfIvy!

Can u tell me any method other than using coordinate geometry ??because i got this question to solve in a circles paper.
Also, I don't know how the equation of circle is .
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