1. The problem statement, all variables and given/known data Hi guys. Just before I ask I wanna tell you my situation. Im doing a course in Astronomy in London, and as much as i'd say I was pretty good at physics and am highly interested unfortunatley maths is a turbulant subject for me. Unsuprisingly I didnt do too well in my first year finals with respect to maths, and failed my two maths modules marginly. Because of this they sent me the papers to do at home, to be follwed up by an interview to see if im capable of moving to second year. Only thing is I have to complete every question, whereas on the exam day there was an option to choose 5 out of 7 blah blah. So now im just having quarms with stuff I left out that I literally could not understand. I just want people to know I might have quite a few questions on this forum, and id like to apologise in advance if it just looks like im taking advantage, but ive done most of these papers now, all I have left is some things I dont get, which I have tried to find a solution myself, but to no avail. So here's my first question, couldnt do it in the exam. A giant parabolic space dome has a roof described by the equation z = 1 - x^2 - y^2 where z is the height above the ground and x and y are horizontal coordinates all measured in km. Calculate the volume of the dome, using cylindrical polar coordinates. There's more of the question, but i'll see if I can do it with a solution to this part. 2. Relevant equations Well im quite aware that x = rcos0 y = rsin0 z = z So the volume element is dv = rdrd0dz 3. The attempt at a solution But in all honesty I do not know where to start, we never did any work on dome structures during term time. But I do understand the process of integration by polar coordinates so I wont need an explanation for that. Thank you.