# Question #726e8

Jan 12, 2015

They have a ratio that only depends on the radius (diameter).

Any circle with a given radius $R$ (=half the diameter $D$)
will have a circumference of $P = 2 \pi R = \pi D$
and a surface area of $A = \pi {R}^{2} = \frac{1}{4} \pi {D}^{2}$

The ratio between the two:

Surface/Circumference=$\frac{A}{P} = \frac{\pi {R}^{2}}{2 \pi R} = \frac{R}{2} = \frac{1}{2} R$

Circumference/Surface=$\frac{P}{A} = \frac{2 \pi R}{\pi {R}^{2}} = \frac{2}{R}$

Since radius $R$ translates to half the diameter $D$:

$\frac{A}{P} = \frac{1}{4} D$ and $\frac{P}{A} = \frac{4}{D}$