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1. i am revising for the physics aptitude test for oxford and came across this question. it's quite easy and yet i really don't get what i'm doing wrong:

In the figure below, the radius of the larger circle is twice that of thesmaller circle. Find an expression for the fraction of the area of thesquare which is occupied by the two circles.

The figure can be seen on question 12 of the maths section of the paper through this link: https://www2.physics.ox.ac.uk/sites/...2006-Paper.pdf

What I did was

area of square= (5r)^2=25r^2
area of bigger circle = 4pir^2
area of smaller circle = pir^2

total area that the circles occupy = 5pir^2
5pir^2/25r^2 = pi/5

but that's not even close to the answer and idk how
2. (Original post by tanyapotter)
i am revising for the physics aptitude test for oxford and came across this question. it's quite easy and yet i really don't get what i'm doing wrong:

In the figure below, the radius of the larger circle is twice that of thesmaller circle. Find an expression for the fraction of the area of thesquare which is occupied by the two circles.

The figure can be seen on question 12 of the maths section of the paper through this link: https://www2.physics.ox.ac.uk/sites/...2006-Paper.pdf

What I did was

area of square= (5r)^2=25r^2
area of bigger circle = 4pir^2
area of smaller circle = pir^2

total area that the circles occupy = 5pir^2
5pir^2/25r^2 = pi/5

but that's not even close to the answer and idk how
how?
3. (Original post by TeeEm)
how?
that is the incorrect part of my answer but i don't know how.
if the radius of the bigger circle is 2r and the smaller circle is r then won't the side of the square be 5r? the bigger circle, from top to bottom, takes up 4r and the smaller circle r,...?
4. (Original post by tanyapotter)
that is the incorrect part of my answer but i don't know how.
if the radius of the bigger circle is 2r and the smaller circle is r then won't the side of the square be 5r?
post a diagram with what you are doing
5. (Original post by tanyapotter)
that is the incorrect part of my answer but i don't know how.
if the radius of the bigger circle is 2r and the smaller circle is r then won't the side of the square be 5r? the bigger circle, from top to bottom, takes up 4r and the smaller circle r,...?
What is the solution we are trying to get?
6. (Original post by TeeEm)
post a diagram with what you are doing
7. (Original post by Eux)
What is the solution we are trying to get?
10pi / 27+18root2
8. (Original post by tanyapotter)
I got around 0.5989 ... (pain to type the exact answer)
9. (Original post by tanyapotter)
10pi / 27+18root2
Okay, thats fine. You are getting the side of the square wrong. You are not working the side of the square out correctly. Try and find the distance from the centre of the big circle to the top left corner, and the distance from the centre of the small circle to the bottom right corner, as you can then work out the diagonal of the square, and with that the sides. Remember that the diagonal of a square is root 2 * its side length
10. (Original post by TeeEm)
I got around 0.5989 ... (pain to type the exact answer)
Yeah thats right
11. (Original post by TeeEm)
I got around 0.5989 ... (pain to type the exact answer)
could you help me understand why my diagram is wrong? why is the side of the square incorrect?
12. (Original post by Eux)
Okay, thats fine. You are getting the side of the square wrong. You are not working the side of the square out correctly. Try and find the distance from the centre of the big circle to the top left corner, and the distance from the centre of the small circle to the bottom right corner, as you can then work out the diagonal of the square, and with that the sides. Remember that the diagonal of a square is root 2 * its side length
i do know that my side of the square is wrong, but i don't know why. and yes that's how you work it out - find the distance from the centres of the circles to the two corners, then add them to the radii to get the full diagonal of the square and use pythagoras to find the side of the square
but why can't it be 2r + 2r + r? sorry if this is a dumb question but i don't understand why i can't use the diameters of both circles to measure the length of a side
13. (Original post by tanyapotter)
could you help me understand why my diagram is wrong? why is the side of the square incorrect?
It looks that Eux is trying to "evict me" and he looks "extra keen".
I leave you to his "capable" hands.

All the best
14. (Original post by TeeEm)
It looks that Eux is trying to "evict me" and he looks "extra keen".
I leave you to his "capable" hands.

All the best
Noooo come back! You're way more qualified than me
15. (Original post by tanyapotter)
i do know that my side of the square is wrong, but i don't know why. and yes that's how you work it out - find the distance from the centres of the circles to the two corners, then add them to the radii to get the full diagonal of the square and use pythagoras to find the side of the square
but why can't it be 2r + 2r + r? sorry if this is a dumb question but i don't understand why i can't use the diameters of both circles to measure the length of a side
You are making an assumption that just isn't true- can you give any proof that the side of the square = the diameter of the big circle and the radius of the little circle other than just by inspection of the diagram?
16. (Original post by Eux)
Noooo come back! You're way more qualified than me
I was only joking ...
I just woke up from a nap and need to wake up, plus my "to do tray" on my desk is getting taller by the day.
17. (Original post by Eux)
You are making an assumption that just isn't true- can you give any proof that the side of the square = the diameter of the big circle and the radius of the little circle other than just by inspection of the diagram?
just before i read this i understood!! i assumed that the end of the bigger circle is directly in line with the centre of the smaller one, but i literally got my ruler out and checked and there's actually a small gap in between. what a stupid mistake
thank u!!
18. (Original post by TeeEm)
I was only joking ...
I just woke up from a nap and need to wake up, plus my "to do tray" on my desk is getting taller by the day.
Um. It's 9 o clock. And its a saturday...
19. (Original post by Eux)
Um. It's 9 o clock. And its a saturday...
older people get tired ...
20. (Original post by tanyapotter)
i am revising for the physics aptitude test for oxford and came across this question. it's quite easy and yet i really don't get what i'm doing wrong:

In the figure below, the radius of the larger circle is twice that of thesmaller circle. Find an expression for the fraction of the area of thesquare which is occupied by the two circles.

The figure can be seen on question 12 of the maths section of the paper through this link: https://www2.physics.ox.ac.uk/sites/...2006-Paper.pdf

What I did was

area of square= (5r)^2=25r^2
area of bigger circle = 4pir^2
area of smaller circle = pir^2

total area that the circles occupy = 5pir^2
5pir^2/25r^2 = pi/5

but that's not even close to the answer and idk how
Was doing the same paper :
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