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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