areas of circles within circles

[the guy]

I'm trying to construct something and i have confused myself, I can't remember my maths lessons! So I'm stuck on how to work something out...

 

If there are two circles, one within the other (lets call the outer circle 'O' and the inner circle 'I'),

 

If circle I has a radius of 2cm,

 

What should the radius of O be, so that the area of I is equal to the area of O - I?

 

 

 

your help would be very, well, helpful!

 

thanks in advance

[timo]

You already mentioned the way to solve your problem yourself: I = O-I (edit: where O and I in this case stand for the areas of the circles O and I, respectively). Start with that, rewrite it in terms of the radii of the two circles and solve for the radius of the outer circle. Since you already have 277 posts here I assume you know that there is a dedicated "homework help" section, and that this is not homework.

Edited March 5, 2012 by timo

[the guy]

I tried that, and got two different areas...

 

and yes i know there is but this isn't homework...

[Schrödinger's hat]

I tried that, and got two different areas...

 

and yes i know there is but this isn't homework...

 

regardless, we can't tell you what you're doing wrong if we don't know what you did

try posting your working

[DrRocket]

I'm trying to construct something and i have confused myself, I can't remember my maths lessons! So I'm stuck on how to work something out...

 

If there are two circles, one within the other (lets call the outer circle 'O' and the inner circle 'I'),

 

If circle I has a radius of 2cm,

 

What should the radius of O be, so that the area of I is equal to the area of O - I?

 

 

 

your help would be very, well, helpful!

 

thanks in advance

 

Let the capital letters represent the areas in which you are interested.

 

If

 

I=O-I

 

then you should be able to solve for I in terms of O. You should also be able to represent I and O in terms of the radii of the associated circles. From that the answer ought to become apparent.

[Ben Banana]

Most simply:

I = O-I

I+I = O

O = 2I

 

Make 'I' a constant.

r = 2 cm

I = pi*r² = 4pi cm²

 

Find O:

O = 2I = 8pi cm²

 

Testing it is easy too.

I = O - I

4 = 8 - 4

4 = 4 indeed.

 

BTW I should learn LaTeX.

 

Edit:

Oh sorry, the radius of O? sqrt(8)

Edited March 5, 2012 by Ben Bowen

[the guy]

ah, thank you, that's made it clear now, i shall try and remember in future too!