Question

Water is flowing through a cylindrical pipe of internal diameter 2cm, into a

cylindrical tank of base radius 40 cm at the rate of 0.7m/sec. By how

much will the water rise in the tank in half an hour?​

Answer 1

Answer: 395.64 liters

Steps:

Volume of Water flowing through the pipe is given by the formula:

• Cross Sectional Area of the Pipe × Rate of Flow

According to the question,

Diameter of the pipe is 2 cm. Hence the cross sectional area of the pipe can be calculated as:

→ Area of Circle = πr²

→ Area of Circle = 3.14 × 1 × 1 = 3.14 cm²

Hence Volume of water flowing per second is given as:

→ Volume = 3.14 cm² × 0.7 m/s ( 70 cm/s )

→ Volume = 219.8 cm³ / s

Hence 219.8 cm³ of water is flowing per second. Hence for 30 minutes, the amount of water flowing is given as:

→ Volume after 30 minutes = 30 × 60 × 219.8

→ Volume after 30 minutes = 395640 cm³

1 cm³ = 0.001 liter

Hence volume of water in liters is given as: 395.64 liters.

Hence after 30 minutes, the volume of water present in the cylindrical tank is 395.64 liters.

Answer 2

Here, as per the provided question we are asked that, 'How much water will rise in the tank in ½ hr'

So, here we'll have to find an appropriate ans. –

GIVEN :

• Water flowing through a cylindrical pipe of internal diameter = 2cm

• Base radius of cylindrical tank = 40cm

• Rate of cylindrical tank when Base radius is 40cm = 0.7m/sec

TO FIND :

• The water rises in the tank in ½ hour = ?

STEP-BY-STEP EXPLANATION :

Now, first of all we will have to find the litres of water rises in the tank in ½ hour = ?

So, now we will have to apply an appropriate formula (which will be used for solving this query)

Appropriate Formula used :

• Area of circle (parts of tank) × Rate of flow of water in the cylindrical tank

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Hence, we will find the area of the circle including an appropriate formula for area of circle –

➠ Area of the circle = πr²

[ substituting the values as per the formula ]

➠ Area of the circle = 3.14 × 1 × 1 = 3.14 cm²

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Now, we will have to find the volume so that we can find the answer for this question easily –

→ volume = area of the circle × rate of flow of water in the cylindrical tank

[ substituting the values as per the formula ] :

→ volume = 3.14cm² × 0.7m/s

[ 0.7 × 100 ] = (70cm/s)

→ volume = 3.14cm² × 70cm/s

→ volume = 219.8cm³/s

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Here, we have to find the amount of water rises in tank in ½ hour = ?

➠ volume after ½ hour = (in minutes)

➠ Volume = 30 × 60 × 219.8

➠ Volume = 395640 cm³

Now, counting the decimal from right side and then applying the formula as 1cm (3) = 0.001 l

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Therefore, we get the the amount of water rises in half hour (½) hour = 395.64 l (litres).