A simple application of dimensional analysis to mathematics is in computing the form of the volume of an n -ball (the solid ball in n dimensions), or the area of its surface, the n -sphere : being an n -dimensional figure, the volume scales as x, while the surface area, being (n − 1) -dimensional, scales as x. Thus the volume of the n -ball in terms of the radius is C n r, for some constant C n. Determining the constant takes more involved mathematics, but the form can be deduced and checked by dimensional analysis alone.