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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
Expert's answer
Answer is a. 10/7

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Comments

Assignment Expert
22.10.12, 16:21

Dear visitor
You're right, thanks for correcting us

kishan kumar
22.10.12, 14:34

the answer is wrong by this method i m getting 10/7 plz correct it sir.

Assignment Expert
10.08.12, 18:34

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.

Vaishnavi
09.08.12, 13:08

but its not given that the circle's diameter is equal to the diagonal. its only given that its in line with it...

Assignment Expert
20.10.11, 20:13

We were pleased to help you

tanmay
20.10.11, 19:35

thank you sir!

Assignment Expert
20.10.11, 17:13



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.

tanmay
19.10.11, 13:00

can u please provide me with steps please

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