Question

A cylindrical container is filed with her ice cream whose radius is 6 cm & height 15 cm. The whole ice cream is to be distributed among 10 children in equal cones having hemispherical tops. If the height of conical portion is 4 times the radius of its base, Find the radius of the ice cream cone.

Answer 1

Volume of ice cream.

Volume of ice cream$=3.142\times 6^2\times 15$

$=1696.68$

Each child gets $=\frac{1698.68}{10}=169.668c{m}^3$

Take the radius of cone$=$r$=$radius of hemisphere

Height of the cone is therefore$=4r$

Volume of hemisphere$+$volume of cone$=169.668c{m}^3$

$\frac{2}{3}\times 3.142\times r^3+\frac{1}{3}\times 3.142\times r^2\left(4r\right)=169.668$

$2.09r^3+4.19r^3=169.668$

$6.28r^3=169.668$

$r^3=27$

$r=3$cm

$\therefore$ Radius of cone$=3$cm.