Discussion

Explanation:

The height of the two cones is in the ratio 7: 3. 

Also, the ratio of the radii will be the same as the ratio of the diameters. Hence, the ratio of the radii will be 6 : 7. 

For a cone, the volume V is given by,

V = 1/3 × π × r² × h

Hence, the ratio of the volume of the cones will be the product of the ratio of the squares of the radius and the ratio of the heights of the two cones.

i.e., $\frac{{\mathrm{V}}_1}{{\mathrm{V}}_2}$ = $\frac{{{\mathrm{r}}_1}^2}{{{\mathrm{r}}_2}^2}$ × $\frac{{\mathrm{h}}_1}{{\mathrm{h}}_2}$ = $\frac{36}{49}$ × $\frac{7}{3}$ = $\frac{12}{7}$

∴ The ratio is 12 : 7.

Hence, option (b).

» Your doubt will be displayed only after approval.