A conical funnel 24 cm tall is cut by a plane parallel to its base, 8 cm below the apex. Find the ratio of the volume of the frustum left to the volume of the small cone removed.

The small cone is similar to the whole cone with linear scale $\frac{8}{24}=\frac{1}{3}$, so its volume is ${\left(\frac{1}{3}\right)}^3=\frac{1}{27}$ of the whole. The frustum is $1-\frac{1}{27}=\frac{26}{27}$. Ratio frustum : small cone = 26 : 1. 27 : 1 compares the WHOLE cone with the small one; 9 : 1 squares the scale instead of cubing it; 8 : 1 is the answer for a cut at half the height, not a third.