A hemispherical bowl is 176 cm round the brim. Supposing it to be half full, how many persons may be served from it in hemispherical glasses 4 cm in diameter at the top ?

Answer: Option C

Let the radius of the hemispherical bowl be r cm
Then,
$$\begin{array}{rl}& 2\pi r=176\\ & \Rightarrow r=\frac{176\times 7}{2\times 22}\\ & \Rightarrow r=28\end{array}$$
Volume of liquid in the bowl :
$$\begin{array}{rl}& =\frac{1}{2}\times \left(\frac{2}{3}\times \pi \times 28\times 28\times 28\right)\text{ c}{\text{m}}^3\\ & =\left(\frac{2}{3}\times \pi \times 14\times 28\times 28\right)\text{ c}{\text{m}}^3\end{array}$$
Volume of 1 glass :
$$=\left(\frac{2}{3}\times \pi \times 2\times 2\times 2\right)\text{ c}{\text{m}}^3$$
∴ Required number of person :
$$\begin{array}{rl}& =\frac{\text{Volume of liquid in the bowl}}{\text{Volume of 1 glass}}\\ & =\left(\frac{14\times 28\times 28}{2\times 2\times 2}\right)\\ & =1372\end{array}$$