1. The problem statement, all variables and given/known data Consider the region of the x y plane given by the inequality: x^2 + 4x + y^2 - 4x - 8 ≤ 0; If this region rotates an angle of π/6 radians around the line given by the equation x + y = 0, it will create a solid of revolution with surface area equal to (i) (128/3)π; (ii) (128/4)π; (iii) (128/5)π; (iv) (128/6)π; (v) (128/7)π 2. Relevant equations area of a sphere = 4πr^2 3. The attempt at a solution okay, so first I factored the inequality into: (x + 2)^2 + (y - 2)^2 ≤ 16; Which means it's a circle centered at (2, -2) and with r = 4. The line x + y = 0 goes through the center of the circle. Now I am stuck.. cause I though that if it rotated an angle of π radians around the line it would give the full external area of the sphere so if it rotated only π/6 it would give 1/6 of it. Which would equal to (4π4^2)/6 = (64/6)π. But that is not one of the answers..