A vessel in the form of a hemispherical bowl is full of water. Its contents are emptied in a right circular cylinder. The internal radii of the bowl and the cylinder are 3.5 cm and 7 cm respectively. Find the height to which the water will rise in the cylinder.
Correct option is C. $$ \dfrac{7}{12}\,cm $$
Suppose water level rises by h cm. Then,
Volume of a cylinder of radius 7 cm and height h = Volume of bowel
$$ \Rightarrow \pi \times 7^{2} \times h = \dfrac{2}{5} \times \left ( \dfrac{7}{2} \right )^{3} \Rightarrow h = \dfrac{7}{12}cm$$