A cylindrical vessel of height 5 cm and radius 4 cm is completely filled with sand. When this sand is poured out it forms a right circular cone of radius 6 cm. What will be the height of this cone?

(Take $pi=frac{22}{7}$ )

Volume of sand in cylindrical vessel

$=pi r^{2} h=pi imes(4)^{2} imes 5 mathrm{cu} . mathrm{cm} .=80 pi mathrm{cu} . mathrm{cm} .$

According to the question

volume of conical shape = 80S cu. cm.

$Rightarrow frac{1}{3} pi mathrm{R}^{2} mathrm{H}=80 pi$

$Rightarrow frac{1}{3} imes 6 imes 6 imes mathrm{H}=80$

$Rightarrow 12 mathrm{H}=80$

$Rightarrow mathrm{H}=frac{80}{12}=6.67 mathrm{~cm}$