Correct Answer - Option 4 : 18 m
Suppose, the height of the cone of the smallest size to accommodate 20 persons is h meters.
\(20{\rm{}} \times {\rm{}}\frac{1}{3}{\rm{\pi }}{{\rm{r}}^2}{\rm{\;h}} = {\rm{}}20{\rm{}} \times {\rm{}}150\)
⇒ \(20{\rm{}} \times {\rm{}}\left( {\frac{1}{3}{\rm{}} \times {\rm{}}25} \right){\rm{}} \times {\rm{\;h}} = {\rm{}}150{\rm{}} \times {\rm{}}20{\rm{\;}}\)
⇒ \(\frac{{25{\rm{h}}}}{3}{\rm{}} = {\rm{}}150\)
⇒ h/3 = 6
⇒ h = 18 m