A container shaped like a right circular cylinder having diameter 12cm and height 15cm is full of ice cream. The ice cream is to be filled into cones of height 12cm and diameter 6cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

Given:Height (h1) of cylindrical container = 15 cmRadius =Diameter/2Radius (r1) of circular end of container =12/2=6 cmRadius (r2) of circular end of ice-cream cone =6/2=3 cmHeight (h2) of conical part of ice-cream cone =12cmLet n ice-cream cones be filled with ice-cream of the container.Volume of ice-cream in cylinder = n (Volume of 1 ice-cream cone + Volume of hemispherical shape on the top)πr₁²h₁=n(⅓πr₂²h₂+⅔πr₂³)⇒π×6²×15=n(⅓π3²×12+⅔π3³)⇒n=360/108+54⇒n=360/162n=10So, 10 ice-cream cones can be filled with the ice-cream in the container.