Question

Water is pouring into a conical vessel as shown in the adjoining figure at the rate of 1.8 m${}^3$ per minute. How long will it take to fill the vessel?

Answer 1

Given diameter of cone =5.2 m and slant height =6.8 m

Then radius =2.6 m

Then height of cone =$\sqrt{(6.8{)}^2-(2.6{)}^2}$

$=\sqrt{46.24-6.76}$

$=\sqrt{39.48}=6.28m$

Then volume of cone =$\frac{1}{3}\times \frac{22}{7}\times 6.28\times (2.6{)}^2$

$=\frac{22\times 6.28\times 2.6\times 2.6}{7\times 3}$

$=44.48m^3$

Given Rate of 1.8 cub meter per minute

Then time taken=$\frac{44.48}{1.8}=24.71\approx 25$ minute