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YAHM

I'm not after an answer (especially not an approximate one) I need to know how to do the actual problem. Answers are in the back of the book.
 
i don't think you can get a direct answer...something like 10x or something like that cause you can change the size of the middle circle and it'll change the answer
 
Originally posted by: alimoalem
i don't think you can get a direct answer...something like 10x or something like that cause you can change the size of the middle circle and it'll change the answer
Click to expand...

See, that's what I was thinking, but a correct answer is given in the book (25pi if anyone is wondering). Maybe it's a typo in the problem and more information should have been given?
 
I'm pretty sure you can't do that because you can get it from any two circles given they're the right size, and I'm pretty damn sure they're not all going to have the same area.
 
This is one of those problems that at first seems as though you don't have enough information to solve... only to find out you really do.

First of all, let's call the radius of the outer circle 'x', and the radius of the inner circle 'y'.

Thus we have a right triangle with vertices at the intersection of AB and the inner circle, the center of the two circles, and A or B itself. By Pythagoream's Theorem, we have:

5^2 + y^2 = x^2.

Now we know the formal for area of a circle is Pi*r^2, so the area of the inner circle is
Pi * y^2, while the area of the outer circle is Pi * x^2. Hence, the area between them is:

Pi * x^2 - Pi * y^2 = Pi * ( x^2 - y^2).

But from the first equation we know that x^2 - y^2 = 5^2 = 25, so the area between the two circles is 25 * Pi.
 
Originally posted by: MathMan
This is one of those problems that at first seems as though you don't have enough information to solve... only to find out you really do.

First of all, let's call the radius of the outer circle 'x', and the radius of the inner circle 'y'.

Thus we have a right triangle with vertices at the intersection of AB and the inner circle, the center of the two circles, and A or B itself. By Pythagoream's Theorem, we have:

5^2 + y^2 = x^2.

Now we know the formal for area of a circle is Pi*r^2, so the area of the inner circle is
Pi * y^2, while the area of the outer circle is Pi * x^2. Hence, the area between them is:

Pi * x^2 - Pi * y^2 = Pi * ( x^2 - y^2).

But from the first equation we know that x^2 - y^2 = 5^2 = 25, so the area between the two circles is 25 * Pi.
Click to expand...


Well, now I know how you got the name MathMan. 😉
 
Originally posted by: MathMan
This is one of those problems that at first seems as though you don't have enough information to solve... only to find out you really do.

First of all, let's call the radius of the outer circle 'x', and the radius of the inner circle 'y'.

Thus we have a right triangle with vertices at the intersection of AB and the inner circle, the center of the two circles, and A or B itself. By Pythagoream's Theorem, we have:

5^2 + y^2 = x^2.

Now we know the formal for area of a circle is Pi*r^2, so the area of the inner circle is
Pi * y^2, while the area of the outer circle is Pi * x^2. Hence, the area between them is:

Pi * x^2 - Pi * y^2 = Pi * ( x^2 - y^2).

But from the first equation we know that x^2 - y^2 = 5^2 = 25, so the area between the two circles is 25 * Pi.
Click to expand...

Wow well done, thanks mate!
 
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