A cone is cut by a plane parallel to its base. The frustum formed has end radii 20 cm and 15 cm. Find the ratio of the volume of the frustum to the volume of the small cone removed.

The small cone is similar to the whole cone with linear scale $\frac{15}{20}=\frac{3}{4}$, so small : whole = $3^3:4^3=27$ : 64. The frustum is 64 - 27 = 37 parts, so frustum : small cone = 37 : 27. 27 : 37 reverses the order; 64 : 27 compares the WHOLE cone with the small one; 4 : 3 is the linear ratio, not cubed.