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

larger circle?
32 in
40 in.
80 in
160 in.

Answer 1

Answer:40 in

Explanation:

The formula for calculating the circumference of a circle is given as

C = 2πr

Let r be the radius of the smaller circle and R be the radius of the bigger circle, the ratio of their circumference is given as 2 : 5 , this implies that

2πr : 2πR = 2 : 5

Which could be written as
`(2\pi r)/(2\pi R)` =
`(2)/(5)`

r = 16 , the the equation becomes:

`(16)/(R)` =
`(2)/(5)`

Cross multiply

2R = 16 x 5

2R = 80

R = 80/2

R = 40 in