Question

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep. If the water flows through the pipe at the rate of 4 km per hour, in how much time will the tank be filled completely?

Answer 1

$\underline{\bold{Given:}}$

Diameter of pipe = 20cm.

Diameter of tank = 10m

Height of tank = 2m.

$\underline{\bold{To\:Find:}}$

time taken to fill the tank.

The further Answer is given in the attachment .

Answer 2

Answer :

Diameter of cylindrical tank = 10 m

.°. Radius = 5 m

We know that,

Volume of cylinder = π r^2 h

Volume of cylindrical tank

= 22/7 × 5 × 5 × 2

= 1100/7 m^3

Now,

Radius of pipe = 10 cm = 0.1 m

Water flows at => 4 km/hrs = 4000 m/hrs

Now,

Let's assume the length of water column as 'x' metres

We can say that ,

Volume of the water column = 1100/7 m^3

1100/7 = π r^2 h

1100/7 = 22/7 × 0.1 × 0.1 × 'x'

1100/7 = 0.22x/7

Cancelling 7 on both sides,

1100 = 0.22x

5000 = x

Length of water column = 5000 m or 5 km.

Now,

We have to find the time required for the tank to get filled completely.

Time = Distance/Speed

Time = 5 km /(4 km/hrs)

Time = 1.25 hrs

= 1 hrs 15 mins or 75 mins.

Hence, In 75 mins, the tank be filled completely.

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