SOLUTION: Consider two circles, a smaller one and a larger one. If the larger one has a radius that is 5 feet larger than that of the smaller circle and the ratio of the circumferences is 2:

Algebra ->  Circles -> SOLUTION: Consider two circles, a smaller one and a larger one. If the larger one has a radius that is 5 feet larger than that of the smaller circle and the ratio of the circumferences is 2:      Log On


   

Question 1015309: Consider two circles, a smaller one and a larger one. If the larger one has a radius that is 5 feet larger than that of the smaller circle and the ratio of the circumferences is 2:1, what are the radii of the two circles?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
circumference of the smaller circle is 2*pi*r

cicumference of the larger cicle is 2*pi*(r+5)

2*pi*(r+5)/2*pi*r = 2/1

the 2*pi in the numerator and denominator cancel out and you are left with:

(r+5/r = 2/1

cross multiply to get 2*r = r+5

subtract r from both sides of the equation to get 2*r - r = 5

combine like terms to get r = 5.

therefore r+5 = 10.

the radius of the smaller circle is 5 feet and the radius of the larger circle is 10 feet.

circumference of the smaller circle is 2*pi*r = 2*pi*5 = 10*pi.

circumference of the larger circle is 2*pi*r = 2*pi*10 = 20*pi.

circumference of the larger circle is two times the circumference of the smaller circle.

the radii of the two circles are 5 feet and 10 feet.