Question

Water flows at the rate of 10 metre per minute from a cylindrical pipe with 5mm long diameter. How long will it take to fill up a conical vessel whose diameter is 40 cm and depth is 24 cm?

• A. 48 minutes 15 secs
• B. 51 minutes 12 secs
• C. 52 minutes 1 sec
• D. 55 minutes

Answer 1

The correct option is B 51 minutes 12 secs

We have,
Radius of the base of the conical vessel, r = 20 cm
Height of the conical vessel, h = 24 cm
Diameter of cylindrical pipe = 5 mm
$\Rightarrow$ Radius of cylindrical pipe = 2.5 mm
= 0.25 cm
= $\frac{1}{4}cm$

$\therefore$ Volume of the conical vessel$=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times 20\times 20\times 24c{m}^3\dots \left(i\right)$

Suppose the conical vessel is filled in $x$ minutes.
Then, length of the water column in the cylindrical pipe
$=(10\times x)m=1000xcm$
(Since rate of flow of water is 10 metre per minute)

$\therefore$ Volume of the water that flows through the cylindrical pipe in x minutes
$=\frac{22}{7}\times (\frac{1}{4}{)}^2\times 1000xc{m}^3\dots (ii)$
We know that volume of water flowed through the pipe in x minutes will be equal to the volume of the conical vessel (as in x mutes, the conical vessel will be completely filled with water)

from (i) and (ii), we have
$\frac{22}{7}\times (\frac{1}{4}{)}^2\times 1000x=\frac{1}{3}\times \frac{22}{7}\times 20\times 20\times 24c{m}^3$
$\Rightarrow x=\frac{20\times 20\times 24\times 16}{3\times 1000}=\frac{256}{5}=51minutes12secs$

Hence, the conical vessel is filled in $51minutes12secs$.