Question

A hemispherical bowl of internal radius 9 cm is full of water. Its contents are emptied into a cylindrical vessel of internal radius 6 cm. Find the height of water in the cylindrical vessel.

Answer 1

Volume of hemispherical bowl = Volume of cylindrical vessel
Let h be the height of water in cylindrical vessel.
$\frac{2}{3}\pi r^3=\pi \times r^2\times h$

$\frac{2}{3}\times 9\times 9\times 9=6\times 6\times h$
$2\times \times 3\times 81=36\times h$
$6times81=36\times h$
$486=36\times$
$h=\frac{486}{36}$

$h=13.5cm$
Therefore, height of water in cylindrical vessel is 13.5 cm.