Question

A cylindrical container of radius 6 cm and height 15 cm is filled with ice cream. The whole ice cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is 4 times the radius of its base, find the radius of the ice cream cone.

Answer 1

Volume of ice cream $=3.142x{6}^{2}x15=1696.68$

Each child gets $=1696.68/10=169.668c{m}^3$

Take radius of cone = r = radius of hemisphere
Height of cone is therefore = 4r

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

$=\frac{2}{3}\pi r^3+\frac{1}{3}\pi r^{2}h=169.668$

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

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

$6.28r^3=169.668$

$r^3=27$

$r=3cm$

∴ Radius of cone = 3 cm