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 ?

Solution(By Examveda Team)

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