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

## Comments

Assignment Expert22.10.12, 16:21Dear visitor

You're right, thanks for correcting us

kishan kumar22.10.12, 14:34the answer is wrong by this method i m getting 10/7 plz correct it sir.

Assignment Expert10.08.12, 18:34Dear 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.

Vaishnavi09.08.12, 13:08but its not given that the circle's diameter is equal to the diagonal. its only given that its in line with it...

Assignment Expert20.10.11, 20:13We were pleased to help you

tanmay20.10.11, 19:35thank you sir!

Assignment Expert20.10.11, 17:13Draw 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.

tanmay19.10.11, 13:00can u please provide me with steps please

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