If the heights of two cones are in the ratio 7 : 3 and their diameters are in the ratio 6 : 7, what is the ratio of their volumes ?

Let the heights of two cones be 7x and 3x and their radii be 6y and 7y respectively
Then,
Ratio of volume :
$$\eqalign{ & = \frac{{\frac{1}{3}\pi \times {{\left( {6y} \right)}^2} \times 7x}}{{\frac{1}{3}\pi \times {{\left( {7y} \right)}^2} \times 3x}} \cr & = \frac{{36 \times 7}}{{49 \times 3}} \cr & = \frac{{12}}{7}\,Or\,12:7 \cr} $$