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


Answer :




Volume of the cylinder
\(= \ \pi r^2 h \ = \ \pi ( \frac{12}{2})^2 \ × \ 15 \ \)

\( = \ \pi \ × \ 6^2 \ × \ 15 \) cm3

Volume of a cone having hemispherical shape on the top

\(= \ \frac{1}{3} \pi r^2 h \ + \ \frac{2}{3} \pi r^3 \ \)

\( = \ \frac{1}{3} \pi r^2 (h \ + \ 2r) \)

\( = \ \frac{1}{3} \pi ( \frac{6}{2})^2 (12 \ + \ 2 \ × \ \frac{6}{2} ) \ \)

\( = \ \frac{1}{3} \pi \ × \ 3^2 \ × \ 18 \) cm3

Let the number of cone that can be filled with ice cream be n.

Then, \( \frac{1}{3} \pi \ × \ 3^2 \ × \ 18 \ × \ n \ = \ \pi \ × \ 6^2 \ × \ 15 \)

\( \Rightarrow \ n \ = \ \frac{\pi \ × \ 6 \ × \ 6 \ × \ 15\ × \ 3 \ }{ \pi \ × \ 3 \ × \ 18 \ × \ 3 \ } = \ 10 \)

\(\therefore \) 10 cones can be filled with ice cream.

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