# Find the Mass

Calculus Level 4

$x = r\cos(\theta)\hspace{1cm}y = r\sin(\theta)\hspace{1cm}z = z$ $0\leq\,r\leq\sqrt{z}\hspace{1cm}0\leq\,\theta\leq2\pi\hspace{1cm}0\leq\,z\leq1$

A solid object exists within the standard $$(x,y,z)$$ coordinate system. Its geometry is parametrized as shown above.

The object has a mass density $$\large {\rho = e^{z^{2}}}$$, where $$e$$ is Euler's number. The objects mass can be expressed as:

${\dfrac{\pi}{A} (e - B)},$

where $$A$$ and $$B$$ are integers, determine $$A+B$$.

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