Question

A vessel in the form of a hemispherical bowl is full of water. The contents are emptied into a cylinder. The internal radii of the bowl and cylinder are respectively 6 cm and 4 cm. Find the height of water in the cylinder.

Answer 1

Radius of hemispherical bowl (r) = 6 cm

$\therefore$ Volume of water in it $=\frac{2}{3}\pi r^3=\frac{2}{3}\pi (6{)}^{3}c{m}^3$

= $\frac{2}{3}\times 6\times 6\times 6\pi c{m}^3=144\pi c{m}^3$

Now volume of water in cylinder $=144\pi c{m}^3$

Radius (R) = 4 cm

$\therefore Height=\frac{volume}{\pi r^2}$

=$\frac{144\pi }{\pi \times 4\times 4}$ = 9 cm

Hence height of water in cylinder = 9 cm