Question

Water flows at the rate of 5 m per minute through a cylindrical pipe, whose diameter is 7 cm. How long it will take to fill the conical vessel having base diameter 21 m and depth 12 m?

Answer 1

Answer:

It will take 1200 hrs to fill the vessel.

Step-by-step explanation:

Given:

diameter of the base of the conical vessel = 21 m

radius of the base of the conical vessel r = $\frac{21}{2}\ m$

height of the conical vessel = 12 m

Now we know the formula of Volume of conical vessel

volume of the conical vessel =  $\frac{1}{3} \pi r^2h$

Substituting the values we get;

volume of the conical vessel = $\frac{1}{3} \times \pi \times\frac{21}{2} \times \frac{21}{2} \times12 \ \ \ \ \ equation\ 1$

Also Given:

Diameter of Cylindrical pipe = 7 cm

Radius of  Cylindrical pipe = $\frac{7}{2} \ cm$

Now we know that 1 cm = 0.01 m

Hence  Radius of  Cylindrical pipe = $\frac{7}{200} \ m$

Let the conical vessel is filled in x minutes.

Then, length if the water column = $5x\ m$

Hence water column forms a cylinder of length $5x\ m$ and radius $\frac{7}{200} \ m$

So, Volume of water that flows in x minutes is given by = $\pi r^2h$

Volume of Water that flows in x minutes = $\pi \times \frac{7}{200} \times \frac{7}{200} \times 5x$

We will find the value of x by saying volume of the conical vessel is equal to Volume of Water that flows in x minutes.

Hence,

$\frac{1}{3} \times \pi \times\frac{21}{2} \times \frac{21}{2} \times12 = \pi \times \frac{7}{200} \times \frac{7}{200} \times 5x$

$x=72000\ mins$

Since 1 hour = 60 min

$x = \frac{72000}{60}= 1200 \ hrs$

Hence it will take 1200 hrs to fill the vessel.