Correct spelling, explanation: the English volume is based on the Latin volumen. As it usually is with words of Latin origin, the word has lost the characteristic n at the end, to make place for a much more practical e in English. Thanks to that, the speakers can intuitively know that -ume in volume is read the same way as similar words such as perfume or legume.

Definition of volume:
noun
1. a tome; a book or journal in a series
His Ph.D. article was published in last month’s volume of Medical Journal.
2. loudness of sound
My earphones are broken, I can barely hear anything even at the highest volume.
3. the amount of space taken by something
I style my hair to give them more volume; I like them full and big.

Idioms with volume:
Sheer volume – a huge amount, which is usually followed by another difficulty it poses
I was shocked by the sheer amount of work there was left to do.

Incorrect spelling, explanation: volumn is not a correct spelling variant of volume. Just consider the structure and potential pronunciation of this word – it would probably be read similarly to column, which should guide you to change it. Volume is the correct spelling not only due to its roots (volumen from Latin) but also based on the fact it guides readers to the correct pronunciation of the word’s ending, which should be analogous to fume.

Incorrect spelling

Incorrect spelling

Incorrect spelling