# The Elliptorus

Calculus Level 5

Consider the solid above. It's completely filled with a liquid of density $$\rho = 1.75\times10^3 \text{ kg/m}^3$$.

Given that $$a = 50\text{ cm}, b= 30\text{ cm}, d =70 \text{ cm}$$, the mass of the liquid in kilograms can be expressed as $$\dfrac AB \pi^\alpha$$ for coprime positive integers $$A,B$$ with integer $$\alpha$$, find the value of $$A + B+ \alpha$$.

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