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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.

1106417_1203481_ans_6217003d136f43e4ac59420062126933.png

Mathematics

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