Let the side of the cube be a units. Since sphere is cut off from the cube, radius of the sphere = \(\frac{a}{2}\) units.
∴ Volume of the sphere = \(\frac43\)π \(\big(\frac{a}{2}\big)^3\)
⇒ VS = \(\frac43\) .\(\frac{πa^3}{8}\) = \(\frac{πa^3}{6}\)cu. units ...(i)
Since the cone is cut off from an identical cube, radius of base of cone = \(\frac{a}{2}\) units height of cone = a units.
∴ Volume of cone VC = \(\frac13\)π \(\big(\frac{a}{2}\big)^2\). a = \(\frac13\)π . \(\frac{a^2}{4}\) . a = \(\frac{πa^3}{12}\) ...(ii)
From eqn. (i) and (ii), we get VS × \(\frac12\) = VC ⇒ VS = 2 VC.