Question

Water flows at the rate of $10$ metre per minute through a cylindrical pipe having its diameter as $5mm$. How much time will it take to fill a conical vessel whose diameter of base is $40cm$ and depth $24cm$.

Answer 1

we have
Volume of the water that flows out in one minute

Volume of the cylinder of diameter $5mm$ and length $10$ metre

Volume of the cylinder of radius $(\frac{5}{2}mm=\frac{1}{4}cm)$ and length $1000cm$

$=\frac{22}{7}\times \frac{1}{4}\times \frac{1}{4}\times 1000{cm}^3$

Volume of a conical vessel of base radius $20cm$ and depth $24cm$

$=\frac{1}{3}\times \frac{22}{7}\times {\left(20\right)}^2\times 24{cm}^3$

Suppose the conical vessel is filled in $x$ minutes

Volume of the water that flows out in x minutes = Volume of the conical vessel

$\Rightarrow \frac{22}{7}\times \frac{1}{4}\times \frac{1}{4}\times 1000\times x=\frac{1}{3}\times \frac{22}{7}\times {\left(20\right)}^2\times 24$

$\Rightarrow x=\frac{512}{10}minutes\Rightarrow x=51minutes12seconds$