# Surface Area Enclosed by Projection

Calculus Level 4

Consider a unit-sphere centered at $$(x,y,z) = (0,0,0)$$. In the same coordinate system, there is a circle with radius $$(r = \frac{1}{2}$$) which lies in the $$xy$$ plane and is centered at $$(0,0,0)$$.

If the circle is projected in the $$+z$$ direction onto the surface of the sphere, the surface area enclosed by the resulting projection can be expressed as $$\pi (a - \sqrt{b})$$.

Determine $$(a+b)$$

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