Explanation:

- A solid right circular cone is divided by a plane parallel to the base at one-third the vertical height from the vertex.

- The height of the smaller cone will be one-third of the whole cone.

- Since the plane is parallel to the base, the radius of the smaller cone is also one-third of the whole cone’s radius.

- The volume of a cone is given by $V=\frac{1}{3}\pi r^{2}h$.

- The volume ratio of two similar cones is the cube of the ratio of their respective dimensions.

- Therefore, the volume ratio is $(1/3{)}^3=1/27$.

- Option 3: 1/27

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