Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2009 · Marks: · Difficulty:
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?
(a)1172
(b)1272
(c)1372
(d)1472
Answer
Answer (as printed): C
Explanation
Let the radius of the hemispherical bowl be $r \mathrm{cm}$. Then, $2 \pi r=176 \Rightarrow r=\frac{176 \times 7}{2 \times 22}=28$. Volume of liquid in the bowl $=\frac{1}{2} \times\left(\frac{2}{3} \times \pi \times 28 \times 28 \times 28\right) \mathrm{cm}^{3}$ $$=\left(\frac{2}{3} \times \pi \times 14 \times 28 \times 28\right) \mathrm{cm}^{3} .$$ Volume of 1 glass $=\left(\frac{2}{3} \times \pi \times 2 \times 2 \times 2\right) \mathrm{cm}^{3}$. ∴ Required number of persons = $\frac{\text { Volume of liquid in the bowl }}{\text { Volume of } 1 \text { glass }}=\left(\frac{14 \times 28 \times 28}{2 \times 2 \times 2}\right)=1372$.