Jerome Fredericks' suggestion is fine.
Obviously, if someone has told you "this is wrong, rephrase it," then rephrase it.
As a US native speaker with some science and engineering background, I don't think it needs to be rephrased. I believe the phrase as you have given it, "a column whose diameter is 1 cm." is correct and natural.
A web search turns up many examples in textbooks and similar sources:
"...The power contained in a beam whose diameter is given..." 2008 textbook.
"...it moves with constant speed when pulled horizontally by a force whose magnitude is 3 N..." 2011 textbook.
"...a force whose duration is 0.5 s...," sample exam question.
"...Plutonium, like bismuth, is an element whose density as a liquid is greater than that of the solid at the melting point..." 1959 textbook.
"...Which of these indicators can distinguish between a solution whose pH is 4.6 and a solution whose pH is 7.9?..." 2006 textbook
"...An orbit whose eccentricity equals 0 is circular..." 2015 textbook.
"...Calculate Γ for a European call option for a security whose current price is $205..." 2012 textbook.
I see that there's a long usage note about this in the American Heritage dictionary,
They comment that "This use of 'whose undoubtedly serves a useful purpose, since 'which' and 'that' do not have possessive forms, and the substitute phrase 'of which' is often cumbersome."
To be, personally trying to avoid "whose" in examples like yours and the above is pedantic. The objection that "who" ought to refer only to people doesn't carry much weight, given the plain fact that it _is_ used to refer to inanimate objects, frequently, by well educated professional writers.