This question is the combination of cylindrical structure and cone structure by using given parameters we will find the final radius of the cone. Question from RS Aggarwal book, page number 787.
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, then find the radius of the ice-cream cone.
Volume of ice cream = πr²h
Volume of ice cream = 3.142 x 6² x 15
Each child gets = 1696.68/10 = 169.668 cm³
Take radius of cone = r = radius of hemisphere
∴ Height of cone = 4r
Volume of hemisphere + volume of cone = 169.668 cm³
2/3 x 3.142 x r³ + 1/3 x 3.142 x r² (4r) = 169.668
2.09r³ + 4.19r³ = 169.668
6.28r³ = 169.668
r³ = 27
r = 3 cm
∴ Radius of cone = 3 cm