Question

A farmer connect a pipe of internal diameter 20cm from a canal into a cylindrical tank in her field ,whichis 10m in diametre and 2m deep. If water flows through the pipe at the rate of 3km/h ,howmuch time will the tank be filled ?​

Answer 1

${\bold{\boxed{\boxed{Answer= \:100 minutes.}}}}$

$\begin{lgathered}\bold{Given} \begin{cases} \underline{ \footnotesize\sf{ \star\:Dimensions{\star}:}}\\\ \sf{Internal\:diameter\:of\:the\:pipe\: =20cm}\\\sf{Diameter\:of\:cylindrical\:tank\:=10m} \\\sf{Depth\:of\:tank\: =4m} \\ \sf{Flow \: of \: water \: through \: pipe \: = 3\:km/h} \scriptsize \sf \\ \sf{find \:in \: how\:much\:time\:the\:tank\: will\:be \: filled.}\end{cases}\end{lgathered}$

Solution : Internal diameter of the pipe 20 cm = $\sf\cancel\dfrac{20}{100} = \frac{1}{5}$

$\implies$ Internal radius = $\frac{1}{2}\times\frac{1}{5}=\frac{1}{10} m$

$\implies$ we have, rate of flow of water= 3km/h = 3000 m/h.

$\implies$ Now, Let the pipe take t hours to fill up the tank.

Volume of water that flows in t hours from the pipe.

$\implies$ Area of the cross section × speed × time

$\implies$ πr² × speed × time

$\implies$ $π(\frac{1}{100})\times3000\times\:t$ = 30 πt

$\implies$ Here, Diameter of the tank = 10 m .

$\implies$ Depth = 2 m

$\implies$ Volume of the tank = πr²h = π × (25)2 = $50π\:m^{3}$

$\implies$ Now, volume of the water that flows from the pipe in t hours = Volume of the tank

$\implies$ $\therefore$ 30πt = 50π

$\therefore$$t=\frac{50}{30}\:hours=\frac{50}{30}\times60=100\:minutes$

Answer 2

$\bf{\Huge{\underline{\boxed{\sf{\green{ANSWER\::}}}}}}$

Given:

A farmer connect a pipe of internal diameter 20cm from a canal into a cylinder tank in her field, which is 10m in diameter and 2m deep. If water flows through the pipe at the rate of 3km/hrs.

To find:

The time will the tank be filled.

$\bf{\large{\underline{Explanation\::}}}}}}$

Let the length of pipe for filling whole tank be h m.

A farmer connect a pipe of internal diameter 20cm from a canal into a cylinder tank in her field,

Volume of pipe = Volume of tank.

• Volume of pipe:

We know that formula of the volume of cylinder: πr²h     [cubic units]

We have,

• Diameter of internal pipe= 20cm
• Height of the pipe= h m

Radius of the Internal pipe= $\cancel{\frac{20}{2} }cm$

Radius of the internal pipe= 10cm

[covert into m]

We know that 1cm= $\frac{1}{100} m$

So,

10cm = $\frac{10}{100} m$

Radius of the internal pipe= $\frac{1}{10} m$

Therefore,

→ Volume of pipe= π×$(\frac{1}{10} )^{2}$×h

→ Volume of pipe= $(\pi *\frac{1}{100} *h)m^{3}$

→ Volume of pipe= $\frac{\pi h}{100} m^{3}$

• Volume of tank:

We know that formula of the volume of cylinder: πr²h   [cubic units]

We have,

• Diameter of the tank= 10m
• Height of the tank= 2m

Radius of the tank=$\cancel{\frac{10}{2} }m$

• Radius of the tank= 5m

→ Volume of the tank= π× (5m)² × 2m

→ Volume of the tank= π× 25m² × 2m

→ Volume of the tank= π 50m³

So,

Volume of pipe = volume of tank

→ $\frac{\pi h}{100} =\pi 50$

→ $h=\frac{50\pi*100 }{\pi }$

→ $h=\frac{50\cancel{\pi }*100}{\cancel{\pi }}$

→ h= (50× 100)m

→ h= 5000m

→ h= 5km

Now,

If water flows through the pipe at the rate of 3km\hrs.

→ 3km travels in pipe= 1 hour

→ 1km travel in pipe= $\frac{1}{3} hour$

→ ∴5km travel in pipe= $\frac{5}{3} hour$

• We know that 1 hour= 60 mnutes,

→ $(\frac{5}{3} *60)minutes$

→ $(\frac{5}{\cancel{3}} *\cancel{60})minutes$

→ (5× 20) minutes

→ 100 minutes

Thus,

⇒ 1 hour 40 minutes required time will the tank be filled.