Water flows at the rate of 10 m/minutes through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?
Given:
Water flows at the rate of 10 m/minutes through a cylindrical pipe 5 mm in diameter.
Diameter of the conical vessel $=40\ cm$
Depth of the conical vessel $=24\ cm$.
To do:
We have to find the time it takes to fill the conical vessel.
Solution:
Rate of water flow $= 10\ m/min$
$ = 1000\ cm/min$
Radius of the cylindrical pipe $=\frac{5}{10 \times 2}$
$=0.25 \mathrm{~cm}$
This implies,
Area of the face of the pipe $=\pi r^{2}$
$=\frac{22}{7} \times(0.25)^{2}$
$=0.1964 \mathrm{~cm}^{2}$
Radius of the conical vessel $R=\frac{40}{2}$
$=20 \mathrm{~cm}$
Depth of the conical vessel $H=24 \mathrm{~cm}$
Therefore,
Volume of the conical vessel $=\frac{1}{3} \pi R^{2} H$
$=\frac{1}{3} \times \frac{22}{7} \times(20)^{2} \times 24$
$=\frac{211200}{21}$
$=10057.14 \mathrm{~cm}^{3}$
Time taken to fill the conical vessel $=\frac{\text { Volume of the conical vessel }}{\text { Area of the face of pipe } \times \text { Speed of water }}$
$=\frac{10057.14}{0.1964 \times 10 \times 100}$
$=51.20 \mathrm{~min}$
$=51 \mathrm{~min} \frac{20}{100} \times 60 \mathrm{~s}$
$=51 \min 12 \mathrm{~s}$
The time it takes to fill the conical vessel is 51 minute 12 seconds.
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