A conical funnel is redesigned so that its base radius is made three times as large, while its vertical height is left exactly as before. The new funnel holds how many times as much as the old one?

A cone holds (1/3)π$r^2$h. Only $r$ changes, and it appears SQUARED, so tripling it multiplies the capacity by $3^2=9$ while the 1/3, the π and the height all cancel. The trap 3 times scales the capacity by the linear factor, forgetting that the radius is squared; 27 times cubes the factor, which would be right only if all three dimensions were tripled; 6 times doubles the 3, treating the square as a multiplication by 2.