A solid cube of edge 6 cm and a solid sphere have exactly the same surface area. Which of the two has the greater volume? Take π = 3.14.

The cube's surface = $6\times 36=216{\text{cm}}^2$ and its volume = $216{\text{cm}}^3$. For the sphere, $4(3.14)r^2=216$ gives $r^2=17.2$ and $r$ ≈ 4.15 cm, so its volume = $(4/3)(3.14)(4.15^3)$ ≈ $298.6{\text{cm}}^3$. That is 298.6/216 ≈ 1.38, about 38% more. For a given surface area the sphere always encloses the most — no flat-faced solid can beat it. (Equal surfaces do NOT mean equal volumes, so 'equal' is wrong; the cube is the smaller of the two, not the larger; 8% badly undershoots the gap.)