Determining the radius of a concentric circle.

[angela107]

Homework Statement

If two people were to have a pie, cut concentrically, what would the radius of the smaller disk be, such that the two individuals will have equal amounts of pie?.

Relevant Equations

n/a

A concentric cirlce has two circles with the same center, but a different radii.
We are given a pie with radius ##r##. A circular cut is made at radius ##r## such that the area of the inner circle is ##1/2## the area of the pie.

We know that the formula to calculating the area of a circle is ##πr²## or ##a=πr²## where ##a=1/2A##. Using substitution, we can determing a radius that will provide equal amounts of pie.

##0.5A=πr²##

##r²=0.5A/π##

##r= √(0.5A/π)##

Therefore, the two people will have an equal amount of pie if the radius ##r## of this smaller disk is equal to ##√(0.5A/π)##.

Can someone confirm if my work is correct?

 

[phyzguy]

What you write is confusing because you have used the symbol r to mean two different things. You said,"We are given a pie with radius r. A circular cut is made at radius r such that the area of the inner circle is 1/2 the area of the pie." So you used r for both the larger radius and the smaller radius. Why don't you call the radius of the whole pie R? I think your work is correct, but I think your should express your final answer for r in terms of R, and not in terms of the area A. If you do that, what do you get?

 

[Lnewqban]

Assuming that A stands for area of the whole pie, do you need to know A in order to determine r?
Could you make r a function of R only, which is the easiest dimension to know?

 

[Mark44]

Therefore, the two people will have an equal amount of pie if the radius ##r## of this smaller disk is equal to ##√(0.5A/π)##.

This is correct, but you should give r in terms of the radius of the pie, which others in this thread are labelling R.

 

[angela107]

What you write is confusing because you have used the symbol r to mean two different things. You said,"We are given a pie with radius r. A circular cut is made at radius r such that the area of the inner circle is 1/2 the area of the pie." So you used r for both the larger radius and the smaller radius. Why don't you call the radius of the whole pie R? I think your work is correct, but I think your should express your final answer for r in terms of R, and not in terms of the area A. If you do that, what do you get?

Sorry, I didn't notice I had two different R's! I will make a correction. Thank you :)