A solid right circular cone is cut into two parts by a plane parallel to its base and at a point one-third vertically below its vertex. What is the ratio of the volume of the smaller cone to that of the whole cone?

A

$$\frac{1}{9}$$

B

$$\frac{1}{8}$$

C

$$\frac{1}{27}$$

D

$$\frac{1}{3}$$