A cone and a cylinder have the same height and the same volume. Find the ratio of the radius of the cone to the radius of the cylinder.

(1/3)π$R^2$$h$ = π$r^2$$h$ gives $R^2=3r^2$, so $R:r$ = √3 : 1. The cone must be wider, but only by √3 ≈ 1.73 times, because the radius enters squared. (3 : 1 forgets the square and would make the cone hold three times too much; 1 : √3 and 1 : 3 make the cone the narrower of the two, which cannot match a cylinder of the same height.)