Question

Water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Find the time in which the level of water in the tanks will rise by 21 cm.

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Answer 1

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Question:

Water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Find the time in which the level of water in the tanks will rise by 21 cm.

Solution:

In cylinder:

r = 7cm = 0.7m

l = 15km = 15000m

In tank:

l = 50m

b = 44m

h = 0.21 m

WE KNOW THAT:

Volume of water in tank= l × b × h

= 50 × 44 × 0.21

= 462 m²

Height of cylindrical pipe=

$\frac{volume}{\pi {r}^{2} }$

$= \frac{462}{ {(0.07)}^{2} \: \large[\frac{22}{7} ] }$

$= \frac{462}{0.0154}$

$= 30000 \: m$

$Time \: = \: \frac{30000}{15000}$

$= 2 \: hours$

Answer 2

SOLUTION

Let the length of the pipe for filling the whole tank be h m.

(i) pipe is in the form of cylinder where

height =h m

height =h mdiameter =14 cm

⇒14/2 = 7cm = 7/100m

Volume of pipe = volume of cylinder =πr²h

⇒πr²h = π (7/100)²

⇒h= 22/7 × 7/100 × 7/100 × h=

22× 7h³/ 100×100

(ii) Tank is in the form of caloid where l=500m

$b \: = 44m \: \\ h = 21cm = \frac{21}{100} m \: = 0.21m$

[tex]

Volume of the tank =lbh=50×44× 21/100 = 22×21m²

We have volume of pipe = volume of tank

⇒ 22× 7h/ 100×100 = 22×21

⇒h=3×10000m= 30,000/1000km

= 30km

Water in pipe flows at the rate of 15km/hr

30km travels in pipe in 30/15hrs= 2hrs

So, in 2hrs, the tank will be filed.