consider two circles, a smaller one and a larger one. If the larger one has a radius that is 3 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?

Luciano Webster 2022-07-29 Answered
Consider two circles, a smaller one and a larger one. If the larger one has a radius that is 3 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?
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Answers (1)

nezivande0u
Answered 2022-07-30 Author has 16 answers
Begin by diagramming the two circles just as it states in theproblem

Now determine the circumference of each circle
On the Right, we get 2 π(r+3)
On the Left, we get 2 πr
The ratio of these must be 2:1
2 1 = 2 π ( r + 3 ) 2 π r = r + 3 r
now we can use the first and last fractions and use crossmultiplication to solve for r
( 2 ) ( r ) = ( 1 ) ( r + 3 ) 2 r + r + 3 r = 3
which is the radius of the smaller circle
r+3=6is the radius of the larger circle
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