Question

A hemispherical vessel of radius 1.4 m is filled with water at the rate of 1 m${}^3$/2 min. How much time will it take to fill ?

• A. 12 mins 30 sec
• B. 11 mins 30 sec
• C. 11 mins 10 sec
• D. 12 mins 10 sec

Answer 1

The correct option is B 11 mins 30 sec

Given, Solids: Hemisphere
Radius, $r=1.4\text{cm}$
Rate of filling $=1{\text{m}}^3/2\text{min}$

Volume of hemispherical vessel $=\frac{2}{3}\pi r^3=\frac{2}{3}\times \frac{22}{7}\times 1.4\times 1.4\times 1.4=5.74{\text{m}}^3$

Time taken to fill vessel $=\frac{5.47}{1/2}=5.74\times 2=11.48=11.5\text{min}=11\text{mins}30\text{sec}$

The time taken to fill is 11 mins 30 sec.