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Answer to Question #4654 in Geometry for tanmay
Question #4654
A punching machine is used to create a circular hole of diameter 2 unit from a square sheet of aluminum of width 2 unit, as shown in the figure. 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 a diagonal of the square.
The area of the sheet that remains after punching is
a. 10/7 sq.u
b. 22/7 sq.u
c. 5/7 sq.u
d. 9/7 sq.u
The area of the sheet that remains after punching is
a. 10/7 sq.u
b. 22/7 sq.u
c. 5/7 sq.u
d. 9/7 sq.u
Expert's answer
Answer is a. 10/7
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Comments
Dear visitor You're right, thanks for correcting us
the answer is wrong by this method i m getting 10/7 plz correct it sir.
Dear visitor Please, read the answer more attentively. It's stated there that diagonal of the small square(not initial one!)-the square inscribed in the circle equals to diameter.
but its not given that the circle's diameter is equal to the diagonal. its only given that its in line with it...
We were pleased to help you
thank you sir!
Draw a square incribed the circle. ( You have half that square already; 2 sides of that square are the segments created by the circle and the large square) Diameter of the circle is equal to diagonal of that small square. Using small square's diagonal to calculate the its side. Calculate the small square's area. The circle's area = small square's area + 4 additonal pieces ( on the original graph, you can see there are two of them already. After drawing the small square, you will see all) So area of 4 pieces = The circle's area - small square's area If the circle were incribed in the big square, the remain area would be: Big square'area - circle's area However, 2 small pieces is outside the big square, then the remain area will be: (Big square's area - circle's area ) + 2 small pieces And we have known how to calculate each item in the equation as I mentioned above. Hope it helps.
can u please provide me with steps please
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