Question

Water flows at the rate of 10 metre per minute from a cylindrical pipe 5mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth 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,
r = Radius of the base of the conical vessel = 20 cm
h = Height of the conical vessel = 24 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$=(10\times x)m=1000xcm$
$\therefore$ Volume of the water that flows in $x$ minutes$=\frac{22}{7}\times (\frac{1}{4}{)}^2\times 1000xc{m}^3\dots (ii)$

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

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