When piloting a hot air balloon, lift is attained by affecting the volume of the balloon
This is a poor question
the above statement is untrue
But for your purposes I guess you are going to have to treat it as true (see EDTA response)
For those who want to know the truth
Lift in a hot air balloon is due to heating of the air inside which causes it to expand, but the volume of the balloon is fixed. The extra hot air escapes leaving a decrease in the amount of air inside the balloon. Since there is less air but the volume is still the same the density inside the balloon decreases. The difference between the density of the colder outside air and hot inside air causes static lift.
If there are hot air balloons that can expand during flight, they are most uncommon.
For the second part of the question, would you need to be given n?
Maybe I am missing something in the questions.
EDIT
I am so irritated I could eat iron and spit nails