Question

- A cylindrical ice-cream pot of radius 6 cm and height 21 cm is full of
ice cream. The ice cream is to be filled in cones of height 12 cm and
radius 3 cm. Ice cream on the top of the cone has hemispherical stape.
How many such cones can be filled with ice cream?​

Answer 1

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Answer 2

Numbers of cones filled with ice cream     $n=14$

Step-by-step explanation:

Given,

Cylindrical ice cream pot

r=6 cm ,h=21 cm

Ice cream is to be filled in cones with top of the cone is hemispherical shape

r=3 cm, h=12 cm

Let no of ice cream is filled in cones is n.

Solution,

Volume of cylinder=$V=\Pi r^{2}h$

                               $V=\Pi \times 6^{2}\times 21$  

                                $=756\Pi cm^{3}$

Volume of cone=$V_{c}=1/3\times \Pi r^{2}h$

                            $V_{c}=1/3\times \Pi \times 3^{2}\times 12$

                                  $=36\Pi cm^{3}$

Volume of hemisphere=$V_{h}=2/3\times \Pi r^{3}$

                                       $V_{h}=2/3\times \Pi \times 3^{3}$

                                            $=18\Pi cm^{3}$

To find the no of cones to be filled.

               $n\left ( V_{c} +V_{h}\right )=V$

                            $n=V/\left ( V_{c} +V_{h}\right )$

                            $n=756\Pi /\left ( 36\Pi +18\Pi \right )$

                            $n=756\Pi /54\Pi$

                             $n=14$

14 cones to be filled with ice cream.