Question

The circumferences of two circles are in the ratio of 2:5. The radius of the smaller circle is 16 in. What is the radius of the larger circle?

Answer 1

The radius of the larger circle is 40 inches.

Get first the circumference of the smaller circle.
C = 2πr; Where π = pi; r = radius
    = 2(3.14)(16)
C = 100.48

Now get the circumference of the bigger circle using ratio:
   2/5 = 100.48/C
   2C = 502.4
2C/2 = 502.4/2
     C = 251.2

Using the circumference, compute for the radius of the larger circle:
r = C/2π; Where C = circumference; π = pi
  = 251.2/2(3.14)
  = 251.2/6.28
r = 40

To check:
      C = 2(3.14)(40)
251.2 = (6.28)(40)
251.2 = 251.2