Question

A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder. The diameter of the hemisphere is 21 cm and the total height of the vessel is 14.5 cm. Find its capacity.

Answer 1

Diameter of the hemisphere = 21 cm
So, its radius = $\frac{21}{2}=10.5cm$

Total height of the vessel = 14.5 cm
So, height of cylindrical part = Total height - Radius of hemisphere = 14.5 - 10.5 = 4 cm

Capacity of the vessel = Volume of the hemisphere + Volume of the cylinder
$=\frac{2}{3}\pi r^3+\pi r^{2}h=\frac{2}{3}\times \frac{22}{7}\times {10.5}^3+\frac{22}{7}\times {10.5}^2\times 4=2425.5+1386=3811.5c{m}^3$