Why my volume comes out to be zero have i made any calculation error, please check.

Any doubt then you can ask

It is a closed curve so Integration gives you zero . you want to calculate area or volume go by piece to piece. You know that result in vector calculus that potential function give...

not 0 to π .... because in qus it is clearly mention positive quadrant

why not 0 to pi??

your solution is absolutely correct.....only you did mistake in limit

yes volume never zero. if sometimes u got area or volume equal to zero then use symmticity. in your ans u apply limit 0 to π/2 u get correct ans . in this qus first quadrant is gi...

i think you understand where you are take wrong step

you take 0 to 2pi because of that your answer zero

over the +quadrant so limit should be r=0 to r=2 and theta shoud be 0 to pi/2