Thermal Expansion of a gold ring

[thaixicedxtea]

Homework Statement

You somehow manage to get a gold ring with inner diameter 2.26 cm stuck on your finger, even though your knuckle has a diameter of 2.3 cm. The temperature of the ring is 23 degrees C.
To what temperature would you have to heat the ring in order to get it off your finger? The coefficient of linear expansion of gold is 1.42 E -5. Answer in units of C.

Homework Equations

delta L = alpha/coefficient * Lo * delta T

The Attempt at a Solution

Since I'm given the linear expansion coefficient, I figured that I'm going to use the delta L equation. What I'm stuck with is what to do with the diameters given, like how do I figure out the initial length from the diameter...

 

[LowlyPion]

Homework Statement

You somehow manage to get a gold ring with inner diameter 2.26 cm stuck on your finger, even though your knuckle has a diameter of 2.3 cm. The temperature of the ring is 23 degrees C.
To what temperature would you have to heat the ring in order to get it off your finger? The coefficient of linear expansion of gold is 1.42 E -5. Answer in units of C.

Homework Equations

delta L = alpha/coefficient * Lo * delta T

The Attempt at a Solution

Since I'm given the linear expansion coefficient, I figured that I'm going to use the delta L equation. What I'm stuck with is what to do with the diameters given, like how do I figure out the initial length from the diameter...

What is the circumference of the ring?

 

[thaixicedxtea]

C equals pi * diameter, so the circumference of the ring is 2.26 cm * pi = 7.09.
Is that the length? If it is, why?
I must be thinking too hard...