# Calculating pressure inside a solid sphere

A uniform solid sphere has mass $M$ and radius $R$. The pressure $P$ inside the sphere caused by gravitational compression as a function of distance $r$ from the center of the sphere is given by $P(r) = \dfrac ab \cdot \dfrac{GM^2}{\pi R^4} \left( 1 - \dfrac{r^2}{R^2} \right),$ where $a$ and $b$ are coprime positive integers.

Find the value of $a+b$.

Notation: $G$ denotes the universal gravitational constant: $G = \SI[per-mode=symbol]{6.67e-11}{\newton\meter\squared\per\kilogram\squared}$.

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