How Hot Must the Steel Rim Be to Fit Over the Cast Iron Wheel?

[Nai]

Homework Statement

The question is : Wheels for railway cars are made of a disk shaped cast iron body of outer diameter 930.0 mm and a steel rim of inner diameter 927.0 mm at 20 degrees Celsius. To what temperature must the steel rim be heated so that it will just slip over the cast iron body?

Homework Equations

I know we use the linear expansion formula which is :
The change of length=alpha(initial length)( change of temperature)
The alpha would be the coefficient of linear expansion in this case would be the steel's coefficient which is 1.3e-5 K^-1.
I don't think it's possible to get 268.9 degrees for the steel to expand o-o

The Attempt at a Solution

My work:
(930-927)=(1.3e-5)(927)(T-20)
T=268.9 degrees Celsius

I think I'm doing something wrong >___<
If anyone could help me, it would be awesome.
Thank you in advance.

 

[hikaru1221]

I don't think it's wrong. An expansion of 3mm is quite big. The answer is still far away from the melting point of iron (~ 1500 Celsius degrees)