SOLUTION: Two circles have the same center. The radius of the larger circle is 3 units longer than the radius of the smaller circle. Find the difference in the circumference of the two circl

Algebra ->  Circles -> SOLUTION: Two circles have the same center. The radius of the larger circle is 3 units longer than the radius of the smaller circle. Find the difference in the circumference of the two circl      Log On


   

Question 198771: Two circles have the same center. The radius of the larger circle is 3 units longer than the radius of the smaller circle. Find the difference in the circumference of the two circles. Round to the nearest hundredth.
Thanks.
Found 2 solutions by solver91311, powerinthelines:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The radius of the smaller circle is

The radius of the larger circle is

The circumference of the smaller circle is

The circumference of the larger circle is

So subtract


John

Answer by powerinthelines(1) About Me  (Show Source):
You can put this solution on YOUR website!
2(Pi)x-2(Pi)r == (theta)x
Radius of larger circle is x, radius of smaller circle is r.
(r+3)=x
2(Pi)(r+3)-2(Pi)r == θ x
(2(Pi)(r+3))-2(Pi)r == (θ(r+3))
(2(Pi)(r+3))-2(Pi)r == (θ(r+3))
θ = (6(Pi))/(r+3)
(6(Pi))/(r+3) == (2(Pi)(r+3))-C
C == (2 (Pi) (6 + (6 r)+ r^2))/(3+r) == 2(Pi)r
solves to be:
r = -2
2(Pi)(-2+3) - 2(Pi)(-2) = 2(Pi)-((-)4(Pi)) = 2(Pi)+4(Pi) = 6(Pi)