what geometric surface encloses the maximum volume with the minimum surface area
Surface-area-to-volume ratio For a given volume, the object with the smallest surface area (and therefore with the smallest SA:V) is the sphere, a consequence of the isoperimetric inequality in 3 dimensions. By contrast, objects with tiny spikes will have very large surface area for a given volume.
Earth The shape of Earth is approximately oblate spheroidal. Due to rotation, the Earth is flattened along the geographic axis and bulging around the equator.[92] The diameter of the Earth at the equator is 43 kilometres (27 mi) larger than the pole-to-pole diameter.[93] Thus the point on the surface farthest from Earth's center of mass is the summit of the equatorial Chimborazo volcano in Ecuador.[94][95][96][97] The average diameter of the reference spheroid is 12,742 kilometres (7,918 mi). Local topography deviates from this idealized spheroid, although on a global scale these deviations are small compared to Earth's radius: The maximum deviation of only 0.17% is at the Mariana Trench (10,911 metres (35,797 ft) below local sea level), whereas Mount Everest (8,848 metres (29,029 ft) above local sea level) represents a deviation of 0.14%.[n 13]