Question

a farmer connects a pipe of internal diameter 20cm from a canal into a cylindrical tank in her field,which is 10 m in deep. if water flows through the pipe at the rate of 3km/h,in how much time will the tank be filled?
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Answer 1

Correct Question :-

A farmer connects a pipe of internal diameter 20cm from a canal into a cylindrical tank in her field,which is 10 m in diameter and 2m deep. if water flows through the pipe at the rate of 3km/h,in how much time will the tank be filled?

Given:-

• Diameter of Pipe = 20cm → 1/5m

• Height of Cylindrical tank = 2

• Radius of tank = 10m

• speed of flowing water = 3km/h → 3000m/h

To Find:-

• In how much time will the tank be filled ?

Formulae used:-

• Volume of Cylinder tank = πr²h

• Volume of pipe = Area of Cross section × speed × Time ( h = Distance = speed × Time)

Where,

• r = Radius
• h = Height

Now,

→ Radius of Pipe = 1/5 × 1/2 = 1/10

→ Volume of tank = Volume of Pipe

→ πr²h = πr² × speed × Time

→ π × (5)² × 2= π × ( 1/10)² × 3000 × t

→ π × 25 × 2 = π × 1/100 × 3000t

→ 50πm² = 30πt

→ 50m² = 30t

→ t = 50/30

→ t = 5/3h

→ t = 5/3 × 60

→ t = 100minutes

Hence,

The tank will be filled in 100 minutes.

Answer 2

$\huge \bf required \: answer$

• Diameter of pipe - 20 cm ➡️ 20/100 = 1/5 m
• Depth of tank - 10 m
• Rate of water - 3 km/h ➡️ 3000 m/h
• Height of tank - 2 m
• Time - Let the time be t

First we have to find the radius of pipe

$radius \: = \frac{1}{5} \times \frac{1}{2} = \frac{1}{10}$

Now,

Volume of tank = Volume of pipe

$\pi {r}^{2} h = \pi \: {r}^{2} \times speed \: \times time$

$\pi \times \: {(5)}^{2} \times 2 = (1/10)² × 3000 × t$

$\pi \: \times 25 \times 2 = ( \frac{1}{1000} ) \times 3000t$

$5 0\pi {m}^{2} = 30 \pi {t}^{2}$

${50 \: m}^{2} = 30$

$t \: = \frac{50}{30}$

$t \: = \frac{5}{3}$

$t \: = 100 \: min$