Two
The short answer is that it multiplies by 3.
Argument
First take an example. Use the one you were given
The small circle
The small circle starts out with a diameter of 5. So find the circumference.
d = 2r
r = d/2
r = 5/2 = 2.5
Circumference = 2 pi r
Circumference = 2 * 3.14 * 2.5
Circumference = 15.7
The large circle
The large circle has a diameter 3 times as big.
D = 15
r = d/2
r = 15/2
r = 7.5
Circumference = 2 pi r
Circumference = 2 * 3.14 * 7.5
Circumference = 47.1
What are the ratios of these two numbers?
ration = 37.1 / 15.7 = 3
B <<<<< Answer
Three
Short Answer: C
Comment
Think of the conversion as pi radians = 180 degrees just as you would say 3.78 L = 1 US gallon. The definition you have been offered will get you into trouble if you don't read it properly.
Solution
Change the 3/2 * pi radians into 1.5*pi radians
pi radians / 180 = 1.5 pi radians / x where x is the angle in degrees. Divide both sides by pi.
1 / 180 = 1.5 / x Cross multiply
1*x = 180 * 1.5
x = 270
C <<<< answer.
