Can i get some help:The ratio of the circumference of two circles is 2/3. The radius of the smaller circle is 8 inches. What is the radius of the larger circle?

Question

anonymous · Answer

2/3 ?

anonymous · Answer

Thats the ratio 2:3

imstuck · Answer

Ok, I think I got this.  I hope, at least!  If the ratios of the circles is 2:3, it is also 1:1.5.  I like working with a "1" in one of those spots, it makes things easier to understand.  So if the circumference formula is c = 2(pi)(r), and the circumference of the larger circle is 1.5 times greater, than let x = 16 pi (which is the circumference of the smaller circle with  radius of 8) and let the circumference of the larger circle be 1.5x.  Using the values we now know, the circum. of the larger circle is = 1.5x = 2(pi)(r), and x = 16pi (we already solved for that one, remember?) So sub in 16pi for the x in the circum. formula for the larger circle and get 1.5(16pi)=2(pi)(r).  Multiply the 1.5 by 16 to get 24pi; now 24pi = 2(pi)(r).  Divide both sides by 2pi to isolate r and solve for its value and we have r = 24pi/2pi.  Cancelling out the pi in both numerator and denominator gives us 24/2 which is 12.  I believe the radius of the larger circle, from the work done here, is 12.

anonymous · Answer

thanks for the help @IMStuck your great help

imstuck · Answer

My pleasure!  That's why I'm a teacher! I love math and I love to help others understand it!