  Question

A right circular cylinder having diameter $$12cm$$ and height $$15cm$$, is full of ice cream. The ice cream is to be filled in identical cones of height $$12cm$$ and diameter $$6cm$$ having a hemispherical shape on the top. Find the no. of cones required.

Solution

Volume of cylinder $$=\pi r^2h$$                                $$=\pi(6)^2\times15$$                                $$=540\pi$$Volume of ice cream cone $$=$$ Volume of cone $$+$$ Volume of hemisphere                                             $$=\dfrac{1}{3}\pi r^2h+\dfrac{2}{3}\pi r^3$$                                             $$=\dfrac{1}{3}\pi\times(3)^2\times12+\dfrac{2}{3}\pi\times(3)^3$$                                             $$=36\pi+18\pi$$                                             $$=54\pi$$Now,Number of cones $$=\dfrac{Volume\ of\ cylinder}{Volume\ of\ ice\ cream\ cone}$$                              $$=\dfrac{540\pi}{54\pi}$$                              $$=10$$So, number of cones is 10. Mathematics

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