I don't think this goes in the homework section because I don't actually want help answering the question, I want to know what it means! Consider the volume V inside the cylinder x2 +y2 = 4R2 and between z = (x2 + 3y2)/R and the (x,y) plane, where x, y, z are Cartesian coordinates and R is a constant. Write down a triple integral for the volume V using cylindrical coordinates. Include the limits of integration (three upper and three lower). Evaluate the integral to determine the volume V in terms of R. My main problem is when it asks about the cylinder x2 +y2 = 4R2. I'm nearly 100% sure that equation is not actually for a cylinder but for a circle! And I'm not entirely clear on whether I'm integrating two shapes, as in two volume integrals, or it's describing just one big shape. In the latter case, I still don't know where cylinders come into it.