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## Homework Statement

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

## Homework Equations

area of a sphere = 4πr^2

## 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..