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?

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