1. The problem statement, all variables and given/known data Derive the formula for surface area of a sphere using integration of circles 2. Relevant equations Need to get : S = 4πr2 3. The attempt at a solution Consider a sphere of radius r centred on the origin of a 3D space. Let y be an axis thru the origin. The sphere can be sliced into a row of circles with the y axis at their centres. Consider one of these circles. The circumference c of the circle depends on it centre's distance from the origin such that c = 2πr cos θ , where θ is the angle from the origin between the (x,z) plane to any point on the circle's circumference. r cosθ is the radius of the circle. For -r to r, y= r sinθ The Integration the circles circumferences along y from -r to r is 2πr cos θ ∫dy Since y = r sinθ, then dy / dθ = r cosθ , so dy = r cos θ dθ so the integration formula is 2πr2 ∫ (cos θ)2 dθ I don't get the right formula from that integral. There's something wrong with my setting up the integral. I can't see what though. Please give me a hint or two.