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 ?

Answer: Option D

Let the heights of two cones be 7x and 3x and their radii be 6y and 7y respectively
Then,
Ratio of volume :
$$\begin{array}{rl}& =\frac{\frac{1}{3}\pi \times {\left(6y\right)}^2\times 7x}{\frac{1}{3}\pi \times {\left(7y\right)}^2\times 3x}\\ & =\frac{36\times 7}{49\times 3}\\ & =\frac{12}{7}Or12:7\end{array}$$