## Most Efficient Shape for Holding Liquids

[caption id="attachment_6496" align="alignright" width="440"] Spherical Bottle.[/caption] We store liquids in a bottle. So what is the most efficient shape that uses the least glass to store the most liquid? The volume of a sphere divided by its surface area represents the greatest ratio possible of any geometrical object. We want to use the least material to construct the vessel, while it holds the most. How shall we determine what best meets our requirements? Most Efficient Shape We determine what best meets our requirements by logic supported by mathematics. V/S (sphere) = 4/3пr3/4пr2 = r/3 Use, for purposes of comparison and illustration, a cube, whose dimensions are "a" on a side. Then, since its surface area is the area of its six sides, V/S (cube) = a3/6a2 = a/6 Now since…