A cone of radius 5 cm is filled with water . If the water poured in a cylinder of radius 10 cm , the height of the water rises 2 cm , find the height of the cone .

Solution:  Let  the height of the cone be $h$ cm . Then ,

Volume of the cone $=$ $\frac{1}{3}\times \frac{22}{7}\times5 \times5\times h$  $cm^3$

when the water in the cone is poured in a cylinder of radius 10 cm , the height of the water rises to 2 cm .

$\therefore$            Volume of the water = Volume of a cylinder of  radius 10 cm and height 2 cm .

$\Rightarrow$        Volume of the water  $=\frac{22}{7}\times10 \times 10 \times 2$  $cm^3$

But ,       Volume of the cone = Volume of the water

$\therefore$           $\frac{1}{3} \times \frac{22}{7}\times 5 \times5 \times h=\frac{22}{7}\times 10\times 10 \times 2$

$\Rightarrow$                 $h=24 cm$

Hence , the height of the cone is 24 cm .

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