Question

Given a circle with measures of (C, d, and r) and a circle with measures of (C', d', and r'), what is r' if C C' = 3.0 and d = 12.0?

A) 2
B) 4
C) 8
D) 12

EDIT: The answer is A) 2

Answer 1

we know that

The circumference of a circle is equal to

`C=\pi D`

where

D is the diameter of the circle

In this problem we have

the circumference of the circle
`1` is

`C=12\pi\ units` ------> equation A

the circumference of the circle
`2` is

`C'=\pi D'\ units` ------> equation B

and the ratio of the circumference of the circle
`1` to the circumference of the circle
`2` is

`(C)/(C')=3` ------> equation C

Substitute the equation A and equation B in the equation C

`(12\pi)/(\pi D')=3`

`D'=(12)/(3)=4\ units`

Find the radius r'

`r'=D'/2`

`r'=4/2=2\ units`

therefore

the answer is the option A

`2\ units`