# Area

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• Apr 14th 2012, 10:32 AM
HollieMay2600
Area
Sorry this is hard to explain:

I have a quarter of a circle in a square and a smaller quarter of a circle in a square it's a bit like a path the measurements of the outside of the square are 7m.

I need to find out the area of the path.

Thanks in advance
• Apr 14th 2012, 11:25 AM
emakarov
Re: Area
Quote:

Originally Posted by HollieMay2600
I have a quarter of a circle in a square and a smaller quarter of a circle in a square

Like this? (Smile)

Attachment 23602
• Apr 14th 2012, 11:32 AM
HollieMay2600
Re: Area
Attachment 23604

Like this
• Apr 14th 2012, 11:48 AM
emakarov
Re: Area
Since the smaller sector is contained in the larger one, do I understand right that you need to find the area of the larger quarter circle? For this you need to know its radius R; then its area is $\displaystyle \pi R^2/4$.
• Apr 14th 2012, 12:04 PM
HollieMay2600
Re: Area
All i have is that the outer sqaure is 7 and the path is 2m across

so for the outer circle is it pi x 7 squared / 4
and then pi x 5 squared / 4 for the inner circle.

do you take the two numbers from each other is that your area?

then how would you work out the length of the edges on the circle is this possible?

thanks for your help
• Apr 14th 2012, 12:24 PM
emakarov
Re: Area
I only now realized that "path" from post #1 is supposed to mean a part of a ring, or annulus.

Suppose the radius of the bigger sector is R and the radius of the smaller one is r. Then the area of the quarter ring is $\displaystyle \pi R^2/4-\pi r^2/4=\pi/4(R^2-r^2)=\pi/4(R-r)(R+r)$. You are saying that R - r = 2, but unfortunately, this is not enough to determine the ring area. You also need R + r, or, equivalently, R and r separately. The only information I get from the picture is that R < 7 and r < R. So there is not enough information to find the ring area.