Question

A cylindrical water tank of diameter 1.4 m and 2.1 m is being fed by a pipe of diameter 3.5 cm through which water flows at the rate of 2 m/s in how much time will the be filled
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Answer 1

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$\sf\underbrace{Given: }$

A cylindrical water tank of diameter 1.4 m and height 2.1 m is being fed by a pipe of diameter 3.5 cm through which water flows at the rate of 2 metre per second. In how much time the tank will be filled?

$\sf\underline\red{Solution:}$

We have,

• Diameter of cylindrical tank = 1.4 m
• Radius of tank = d/2 = 1.4/2 = 0.7m
• Height of tank = 2.1 m

Diameter of pipe flowing water in tank = 3.5 cm

• Radius of pipe = d/2 = 3.5/2 cm
• Rate of flow of water = 2 m/s

Time taken to fill the tank = volume of tank / volume of pipe × rate of flow

ㅤㅤ$→$$\sf{= πr\:‑\:2h\: / \:(πr\:‑\:2 \:×\: 2)}$

ㅤㅤ$→$$\sf{=\: (π \:×\: 0.7\: ×\: 0.7 \:× \:2.1)}$/$\sf{\:(π\: ×\: 3.5/2 × 3.5/2\: × \:2)}$

ㅤㅤ$→$$\sf{=\: 1.029\: / \:6.125}$

ㅤㅤ$→$$\sf{= \:0.168}$

ㅤㅤ$→$$\sf{= \:1680 \:seconds}$

ㅤㅤ$→$$\sf{= \:28 \:minutes.}$

∴ Time taken to fill the tank is 28minutes.

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$\sf\underbrace{To\: know\:More: }$

Some Formula of Cylinder

Curved surface Area of cylinder = 2πrh.

• → Base Area of cylinder = πr²

• → Both Side base Area of cylinder = 2(πr²)

• → Total Surface Area of cylinder = curvedsurface Area + both side base Area = 2πrh + 2πr² = 2πr (h+r)..

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