# Mr. Mendrin I presume

Calculus Level 3

The below object's surface area and the volume defined by the region lying inside the cylinder $$x^2 + y^2 = 1$$ and inside the sphere $$(x - 1)^2 + y^2 + z^2 = 4$$ can be represented by

$\pi \cdot A^3 \quad \text{ and } \quad \pi \cdot \dfrac{A^4}B - \dfrac{A^6}{B^2} ,$

respectively, where $$A$$ and $$B$$ are coprime positive integers.

Find $$A+B$$.

×