Learn Swedish: Kabeln kostar tjugo kronor rullen. - The cable costs twenty kronor per roll.

In Swedish, unit prices are often expressed simply by putting the unit of measurement in the definite singular form. So, tjugo kronor rullen translates literally to "twenty crowns the roll," which is the standard way to say "twenty kronor per roll."

Is it also correct to use the word per here, like per rulle?

Yes! You can absolutely say Kabeln kostar tjugo kronor per rulle. Both versions are perfectly correct and very common, but using the definite form without a preposition is a distinctly Swedish idiom you will hear constantly in shops and markets.

If the unit of measurement is an ett-word, how does this structure change?

It works exactly the same way: you just use the definite singular form of the ett-word. For example, if the cable were sold by the kilo (ett kilo), you would say Kabeln kostar tjugo kronor kilot.

I have learned to use prepositions for time rates like i veckan (per week). Why is there no preposition before rullen?

Time expressions for rates do require specific prepositions (like i veckan or om dagen). However, physical quantities and measurements used for pricing drop the preposition entirely. You just attach the definite noun directly at the end of the price.