If the heights of two cones are in the ratio 7 : 3 and their diameters are in the ratio 6 : 7, what is the… · ABC26GN4764

Let the heights of the two cones be $7 h$ and $3 h$ and their radii be $6 r$ and $7 r$ respectively. Then, $$\text { Ratio of their volumes }=\frac{\frac{1}{3} \times \pi \times(6 r)^{2} \times 7 h}{\frac{1}{3} \times \pi \times(7 r)^{2} \times 3 h}=\frac{36 \times 7}{49 \times 3}=\frac{12}{7} \text {. }$$ Hence, required ratio = 12 : 7.