Question

Water flows at the rate of $10$ metres per minute from cylindrical pipe $5mm$ in diameter. How long it will take to fill up a conical vessel whose diameter at the base is $30cm$and depth $24cm$

• A. $28$ minutes $48$ seconds
• B. $51$ minutes $12$ seconds
• C. $51$ minutes $24$ seconds
• D. $28$ minutes $36$ seconds

Answer 1

The correct option is A $28$ minutes $48$ seconds

Given:

Diameter of the pipe = 5mm

Speed of water in pipe = 10 m/min

Diameter of conical vessel = 30cm

Depth of conical vessel = 24cm

We know:

$Volumeofcylinder=\pi r^{2}h$

$Volumeofconicalvessel=\frac{1}{3}\pi r^{2}h$

Solution:

$Radiusofthepipe=\frac{5}{2}mm=2.5mm=0.25cm$

$Speedofwaterinpipe=10m/min=1000cm/min$

$Radiusoftheconicalvessel=\frac{30}{2}cm=15cm$

Now,

$Volumeofcylinder=\pi r^{2}h$

$\Rightarrow V_1=\pi r^{2}h$

$\Rightarrow V_1=\frac{22}{7}\times \frac{25}{100}\times \frac{25}{100}\times 1000$

$\Rightarrow V_1=\frac{22}{7}\times \frac{1}{4}\times \frac{1}{4}\times 1000$

$\Rightarrow V_1=\frac{1375}{7}c{m}^3/min$

Also,

$Volumeofconicalvessel=\frac{1}{3}\pi r^{2}h$

$\Rightarrow V_2=\frac{1}{3}\times \frac{22}{7}\times 15\times 15\times 24$

$\Rightarrow V_2=\frac{39600}{7}c{m}^3$

$\therefore Timerequiredtofillthevessel=\frac{\text{capacity of the vessel}}{\text{volume of water flowing per minute}}$

$\Rightarrow Time=\frac{\left(\frac{39600}{7}\right)c{m}^3}{\left(\frac{1375}{7}\right)c{m}^3/min}$

$\Rightarrow Time=\frac{39600}{1375}min$

$\Rightarrow Time=28\frac{4}{5}min$

$\Rightarrow Time=28min48seconds$