Notăm muchia cubului cu a.
Raza sferei va fi jumătate din diagonala cubului, R= a√3/2
[tex]\it \mathcal{V}_{sfer\breve{a}}=\dfrac{4\pi R^3}{3}=\dfrac{4\pi\cdot\Big(\dfrac{a\sqrt3}{2}\Big)^3}{3}=\dfrac{4\pi\cdot \dfrac{a^3\cdot3\sqrt3}{8}}{3}=\dfrac{\dfrac{3\pi a^3\sqrt3}{2}}{3}=\dfrac{\pi a^3\sqrt3}{2}\\ \\ \\ \dfrac{\mathcal{V}_{sfer\breve{a}}}{\mathcal{V}_{cub}}=\dfrac{\dfrac{\pi a^3\sqrt3}{2}}{a^3}=\dfrac{\pi a^3\sqrt3}{2a^3}=\dfrac{\pi\sqrt3}{2}=\dfrac{\sqrt3}{2}\pi[/tex]
