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?

32 in.
40 in.
80 in.
160 in.

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

Explanation: