1. The problem statement, all variables and given/known data How do I find the surface area of a sphere (r=15) with integrals. 2. Relevant equations Surface area for cylinder and sphere A=4*pi*r2. 3. The attempt at a solution I draw the graph for y=f(x)=√(152-x2). A circle for for positive y values which I rotate. I will create infinite many cylinders with the height dx and radius y. The surface area of those dA=2*pi*y*dx then. I know that √(152-x2) so ∫dA=∫[0,15](2*pi*√(152-x2))dx. It's only a half sphere for I multiplie by 2. If I calculate the value by 4*pi*r2. What is my mistake?