Answer:
1/216
Explanation:
The ratio of volumes of similar shapes is the cube of the scale factor. The filled portion of the cone is similar to the entire cone.
Linear scale factor
If the filled height is 1/6 of the total height, the scale factor for linear dimensions is 1/6.
Volume scale factor
The scale factor for the volume is the cube of the scale factor for linear dimensions. it is ...
(1/6)³ = 1/216
The volume of the filled portion of the cup is 1/216 of the volume of the cup.