Could someone give a clue to how I could prove the sphere has minimal surface area for a given volume? Note this is not a homework problem. I saw in a chemistry textbook that water droplets tend to be spherical because each water molecule has a force directed inwards. In order to minimise the number of molecules on the boundary, the water droplet tend to form a sphere because the book claims it has the minimum surface area per volume. I would like to mathematically prove this fact but don't know how to start.