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# IMC question? watch

1. Can you please explain to me the following question? Our test is in two weeks
A sector of a disc is removed by making two straight cuts from the circumference to the centre. The perimeter of the sector has the same length as the circumference of the original disc. What fraction of the area of the disc is removed?

a) pi-1/ pi
b) 1/pi
c) pi/360
d) 1/3
e) 1/2

I can't understand the solutions but they mention including a ratio and I do not understand why
Thanks
2. A cut from the edge of the circle to its centre must be a cut along the circle's radius.

You need to work out the perimeter of the sector that's been cut out, so you'll need the formula for the length of a circular arc.

The question then says that this perimeter is equal to the circumference of the original circle, so you can set this (which you should know) equal to what you found above. Some stuff should cancel, and you should be able to solve for the angle between the two 'straight bits'. You'll need this when working out the area of the sector.

The last bit, which should get you to the correct answer, just wants you to work out the area of the sector as a fraction of the area of the whole circle i.e. (area of sector)/(area of circle), this might be the ratio that the solution is referring to. At this point, lots of stuff should cancel and you should end up with (pi-1)/pi.

As an aside, this is perfectly possible, if a bit ugly, to do if you're measuring angles in degrees. If you know anything about angles in radians, this is a bit cleaner. Radians are AS Maths though - so if you're doing the IMC, you're probably not studying that yet. Might be worth a read though if you're interested.
3. Incidentally, the maths challenges are meant to be fun, rather than being seen as a serious test, and not really something you should be bothering about revising for too much. By all means have a go at some past questions to get you thinking in that sort of way, but try and enjoy it
4. (Original post by Lolgarithms)
Incidentally, the maths challenges are meant to be fun, rather than being seen as a serious test, and not really something you should be bothering about revising for too much. By all means have a go at some past questions to get you thinking in that sort of way, but try and enjoy it
Thanks! I don't think we even have it this year because the teachers haven't mentioned anything but this question really annoyed me because I couldn't get my simplified answer to be correct thanks for your help though
5. (Original post by lordofthehumans)
Thanks! I don't think we even have it this year because the teachers haven't mentioned anything but this question really annoyed me because I couldn't get my simplified answer to be correct thanks for your help though
Did you manage to get there in the end?
6. (Original post by Lolgarithms)
Did you manage to get there in the end?
Yes thanks I did eventually

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Updated: January 27, 2015
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