Question

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.

Answer 1

Radius of hemispherical bowl (r) = 3.5 cm
Volume $=\frac{2}{3}\pi r^3=\frac{2}{3}\pi \times (3.5{)}^{3}c{m}^3=\frac{2}{3}\pi (3.5\left)\right(3.5\left)\right(3.5)c{m}^3=\frac{85.75}{3}\pi c{m}^3$
Now water in the cylindrical vessel
$=\frac{85.75}{3}\pi c{m}^3$
and radius (R) = 7 cm
Height of water $=\frac{Volume}{\pi r^2}$
$=\frac{85.75\pi }{3\times \pi 7\times 7}=\frac{1.75}{3}=\frac{7}{4\times 3}=\frac{7}{12}cm$