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.
Solution:
It is given that
Volume of water in hemispherical bowl = Volume of cylinder
$\frac{2}{3} \pi r_{1}^{3}=\pi r_{2}^{2} h$
$\frac{2}{3} \pi(6)^{3}=\pi(4)^{2} h$
$h=\frac{2}{3} \times \frac{6 \times 6 \times 6}{4 \times 4}$
h = 9 cm