What geometric shape has the largest volume and smallest surface area?
It is indeed a sphere… According to Wikipedia, “The sphere has the smallest surface area among all surfaces enclosing a given volume and it encloses the largest volume among all closed surfaces with a given surface area. For this reason, the sphere appears in nature: for instance bubbles and small water drops are roughly spherical, because the surface tension locally minimizes surface area. ” From MathIsFun.com: “Of all the shapes, a sphere has the smallest surface area for a volume. Or put another way it can contain the greatest volume for a fixed surface area. Example: if you blow up a balloon it naturally forms a sphere because it is trying to hold as much air as possible with as small a surface as possible.” The corollary in the 2-D world is the circle. A circle is the shape that has the largest area for the smallest perimeter. In fact, there is something called the “Isoperimetric Quotient” which is defined as: IQ = 4 π A / P² where: A = area P = perimeter A circle has the maximu
