My Math Forum Punching Machine

 Algebra Pre-Algebra and Basic Algebra Math Forum

 October 16th, 2011, 03:41 AM #1 Member   Joined: Oct 2011 Posts: 81 Thanks: 0 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
 October 16th, 2011, 07:04 AM #2 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 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 $x^2+ y^2= 4$. The point P, since it lies on the circle, along the diameter y= -x, is at $(-\sqrt{2},\sqrt{2})$ and the edges of the metal sheet are given by $x= -\sqrt{2}$ and $y= \sqrt{2}$. Those edges cut the circle again at $(\sqrt{2}, \sqrt{2})$ and $(-\sqrt{2}, -\sqrt{2})$. The line from the origin to $(\sqrt{2}, \sqrt{2})$ 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, $\pi(2)^2/4= \pi$. So the area that has been cut off the circle by going outside the metal sheet, on that side, is $\pi- 2$ and, since the the other side is symmetrical, the whole area punched out is $4\pi- 2(\pi- 2)= 4- 2\pi$. Since the metal sheet has area 4 square units, there will be $4- (4- 2\pi)= 2\pi$ square units left.
 October 16th, 2011, 07:45 AM #3 Member   Joined: Oct 2011 Posts: 81 Thanks: 0 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 $x^2 + y^2= 4$.

 Tags machine, punching

,

,

,

### a punching machine is used to punch a circular

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post krausebj0 Number Theory 1 June 28th, 2013 05:01 AM FreaKariDunk Probability and Statistics 0 December 3rd, 2012 04:49 PM jenifer Applied Math 1 December 28th, 2011 12:08 PM jenifer Applied Math 0 November 2nd, 2011 08:50 AM mcjason Computer Science 0 July 23rd, 2008 07:01 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top