[ 3x^2 = 4R^2 \quad\Longrightarrow\quad x = \frac{2R}{\sqrt{3}}. ]
Discarding the trivial solution (x = 0) (which gave zero volume), she solved
[ V'(x) = 4x\sqrt{R^2 - \tfrac{x^2}{2}} - \frac{x^3}{\sqrt{R^2 - \tfrac{x^2}{2}}}. ]
When the old brass bell of the university’s clock tower struck eleven, Maya slipped the final key into the lock of the library’s rare‑books room. The room smelled of polished oak, leather, and a faint hint of coffee—its only occupants the towering shelves that held the most beloved (and most feared) tomes of the mathematics department.
