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 four times the radius of its base, find the radius of the ice-cream cone.

Explanation

Radius of cylindrical container`=6cm`
Height of cylindrical container `=15cm`
Volume of cylinder` =pir^2h`
`=>pixx36xx15=540 picm^3`
Now, as it has to be divided among 10 children
Dividing volume by `10, => 540/10=54picm^3`
Volume of cone + Volume of hemispherical top = Volume of ice-cream in it.
`=>1/2pir^h+2/3pir^3=pir^2h`
`1/3pir^2h+2/3pir^3=pir^h`
`1/3pir^2(4r)+2/3pir^3=54pi`
`1/3pir^3(4+2)=54pi`
`2r^3=54`
`r=3`

Hence, the radius of icecream cone` =3 cm.`