1. The problem statement, all variables and given/known data Find the volume of the solid bounded by z=x^2+y^2 and z=8-x^2-y^2 2. Relevant equations use double integral dydx the text book divided the volume into 4 parts, 3. The attempt at a solution f(x)= 8-x^2-y^2-(x^2+y^2)= 4-x^2-y^2 i use wolfram and got 8 pi, the correct answer is 16 pi from the text book. I understood the text book version, I see why its dividing into 4 parts since its symmetric about x and y axis, but I dont understand why my method is half of the correct volume. obviously I need to multiply my double integral by 2, but I just don't get the picture, I am confused, am I just getting the volume of the lower paraboloid with my setup like that? what if the upper paraboloid has different volume as the lower paraboloid, for example, the upper function could be z=4x^2+y^2, then multiplying by 2 just doesnt make sense since the top and bottom are not equal to each other. can someone help me out, its been bothering me since yesterday.