# A conical vessel with radius 20 cm and height 30 cm is full of water. The water of the vessel is transferred to cylindrical vessel of radius 8 cm. Find up to what height will the cylindrical vessel fill.

$\text{Volume of the conical vessel }= \frac{1}{3}\pi r^2h\\ =\frac{1}{3} \pi (20^2)30=4000\pi \ cm^3\\ \text{Assume height of the cylinder=H}\\ \text{Volume of the cylinder }= \pi R^2H=\text{Volume of the conical vessel }\\ \pi (8^2)H=4000\pi \ cm^3\\ H=\frac{4000}{64} \ cm\\ H=62.5 \ cm$

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