Question

Water flows at a rate of $10m/minute$ through a cylindrical pipe $5mm$ in diameter. How long would it take to fill a conical vessel whose diameter at the base is $40cm$ and depth $24cm$?

Answer 1

Given: Speed of water flow $=10m/minute$$=1000cm/minute$

Radius of the pipe $=\frac{5}{2}mm=\frac{2.5}{10}cm=0.25cm$

Area of the face (Circular in shape) of pipe $=\pi r^2=\frac{22}{7}\times (0.25{)}^{2}c{m}^2$

Diameter of the conical vessel $=40cm$

So, radius of the conical vessel, $r=20cm$

And, Depth of conical vessel, $h=24cm$

$\therefore$ Volume of the Conical vessel $=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\times \frac{22}{7}\times {20}^2\times 24c{m}^3$

Now, Required time to fill the conical vessel

$=\frac{\text{Volume of the vessel}}{\text{Area of the circular face of pipe}\times \text{Speed of water}}$

$=\frac{\frac{1}{3}\times \frac{22}{7}\times {20}^2\times 24}{\frac{22}{7}\times (0.25{)}^2\times 1000}$

$=\frac{20\times 20\times 8}{0.25\times 0.25\times 1000}$

$=\frac{20\times 20\times 8}{2.5\times 25}$

$=\frac{4\times 4\times 8}{2.5\times 1}$

$=\frac{4\times 4\times 8\times 10}{25}$

$=\frac{4\times 4\times 8\times 2}{5}$

$=51.20$ minute

$=51$ minute and $12$ second [$\because$ $0.20$ minute$=0.20\times 60=12$ second]