Question

A right circular cylindrical tank 9 metre
high is full of water. If water is removed
by a pipe of diameter 6 cm with a
velocity 225 metre per minute, the total
water is removed in 36 minutes. Find
the diameter of the tank.​

Answer 1

Given

☞ Height of the cylindrical tank (h) = 9 m

☞ Radius of the cylindrical tank (r) = ?

☞ Diameter of the pipe = 6 cm

☞ Radius of the pipe = (6/2) cm = 3 cm

☞ Speed of water in the pipe = 225 m /min

☞ Time taken to remove water = 36 min

To find

☞ Diameter of the cylindrical tank

Solution

Let us find out the Volume of tank

Volume of the cylindrical tank = π r² h

▶ Volume = π r² (9)

▶ Volume = 9 π r²

It is given that water flows out at the speed of 225 metre per minute, and it took 36 minutes to remove water completely from the tank

We know that

Distance = Speed × time

Here, the distance travelled by the water is the height of the water in the pipe

So, Height (H) = Speed × time

▶ Height (H) = 225 m/min × 36 min

▶ Height (H) = 8100 m

Volume of the pipe = π R² H

▶ Volume = π × 3 cm × 3 cm × 8100 m

▶ Volume = π × 0.03 m × 0.03 m × 8100 m

▶ Volume = 7.29 π m³

Now, the volume of water removed by the pipe will be equal to the volume of water in the tank

☞ Volume of tank = Volume of pipe

▶ 9 π r² = 7.29 π

* Cancelling π (pi) from both side

▶ 9 r² = 7.29

▶ r² = 7.29/ 9

▶ r² = 0.81

▶ r = √(0.81)

▶ r = 0.9 m (radius of the tank)

We know that

Diameter = 2 × radius

▶ Diameter = 2 × radius of tank

▶ Diameter = 2 × 0.9 m

▶ Diameter = 1.8 m

∴ Diameter of the tank is 1.8 m or 180 cm

Answer 2

$\huge\underline\mathit{Given:-}$

✪ height of the cylindrical tank = 9m

✪ radius of the cylindrical tank = ??

✪ diameter of the pipe = 6cm

✪ radius of the pipe = ??

radius = $\frac{d}{2}$

radius = $\frac{6}{2}$

radius = 3cm

✪ speed of water in the pipe = 225 m/min

✪ time take to remove the water = 36 min

$\huge\underline\mathit{To find:-}$

✪ ✰ diameter of the cylindrical tank...

$\huge\underline\mathit\green{SoLution!!...}$

$\red{\underline\textbf{Volume of the tank...}}$

volume of cylinder = πr²h

volume of the cylindrical tank = π r² (9)

volume of the cylindrical tank = 9πr²

The water flows out from the tank at the speed of 225 m/min and it took 36 minutes to remove completely water from the tank...

$\red{\underline\textbf{we know that,...}}$

Distance = Speed × Time

Here, the distance travelled by the water is the height of the tank...

$\underline\mathit\green{So,...}$

Height = Speed × Time

===✪✰ height = 225 × 36

===✪✰ height = 1,800m

$\red{\underline\textbf{Volume of the pipe...}}$

Volume = πR²h

volume of the pipe = π × 3cm × 3cm × 8100m

volume of the pipe = π × 0.3m × 0.3m × 8100m

volume of the pipe = 7.29 π m²

$\underline\mathit\green{Now,...}$

The volume of the water is removed by the pipe will be equal to the volume of water in the tank...

✪✰ Volume of pipe = volume of tank

• 9πr² = 7.29π
• 9r² = 7.29
• r² = $\frac{7.29}{9}$
• r² = 0.81
• r = √0.81
• r = 0.9m

$\red{\underline\textbf{Hence, radius of the tank is 0.9m...}}$

$\underline\mathit\green{We\:know\:that,...}$

• Diameter = 2 × Radius

✪✰ diameter = 2 × radius of the tank

✪✰ diameter = 2 × 0.9m

✪✰ diameter = 1.8m

Therefore, the diameter of tank is 1.8m...

( we know 1m = 100cm )

• 1.8m = 1.8 × 100
• 180cm

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Thanks!!...❣️✌️

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