A farmer connects a pipe of internal diameter 25cm from a canal into a cylindrical tank in his field, which is 12m

in diameter and 2.5m deep. If water flows through the pipe at the rate of 3.6km/hr, in how much time will the tank

be filled? Also find the cost of water, if the canal department charges at the rate of Rs0.07/m3

?

R = radius of cylinder = 6m

H = height of cylinder = 2.5m

r = radius of pipe = 25/2cm =1/8m

Rate of flow of water = 3.6km/hr

In 1 hr water upto a length of 3.6km = 3600m will come out of pipe.

let the tank be filled in 'x' hrs.

volume of water coming out of pipe in x hrs = volume of cylindrical tank.

(22/7)(1/8)(1/8)(3600)(x) = (22/7)(6)(6)(2.5)

          (1/8)(1/8)(3600)( x) = 6 x 6 x 2.5

                             3600(x) = 36 x 2.5 x 8 x 8

                                100(x) = 8 x 8 x 2.5

                               1000(x) = 8 x 8 x 25

                                         x = 16/10 = 1.6 hrs

                                        x = 1 hr.36 min.

Now,

            cost of water = volume of cylindrical tank x 0.07

                                   = 22/7 x 6 x 6 x 2.5 x 0.07

                                   = Rs.19.80.

 

    The tank will be filled in 1hr.36 min and the cost of water will be Rs.19.80.

 

[ For reference-refer for-"Me n Mine CBSE Sample Papers-Page 15-google books result]                                    

                                             

  • 39

3.6 km/hr = 5/18*3.6 = 1 m/sec

25 cm = 25/100 m = 0.25 m

Radius = 0.125 m

Volume  = 22/7*0.125*0.125*1 = 0.34375/7 m3

Volume Of Second Tank = 22/7*6*6*2.5 =1980/7

time = 1980/7*7/0.34375 = 5760 seconds = 96 minutes

Amount Of Water To Be Filled = 1980/7 m3

=> 1980/7*0.07 = Rs 19.8

  • -2

Let x hours be the time taken for the pipe to fill the tank.

Since the water is flowing at the rate of 3 Km/h, Therefore,

Length of the water column in x hours is 

Therefore, the length of the pipe is 

The radius of the pipe is

Therefore, the volume of the water flowing through the pipe in x hours is

Also, Volume of the water that falls into the tank in x hours is

We have the volume of the water flowing through the pipe in x hours = Volume of the water that falls into the tank in x hours

Thus equate equations (1) and (2)

Thus, the water in the tank will fill in 100 minutes.

  • -8

vivek tripathi answer is not right

the answer of indhumathi and prakhar are right

but no need to worry.

keep on trying k?

  • 2

Vivek Tripathiyou are wrong

This site has no rating
  • -4

but keep trying

  • 0
Diameter of the cylindrical tank = 10 m Radius of the cylindrical tank (R) = 5 m Height of the cylindrical tank (H) = 2 m Volume of cylindrical tank = π r2H = π × 52 × 2 = 50 π m3 Internal Diameter of the pipe (d) = 20 cm Internal Radius of the pipe (r) = 10 cm = m Rate of flow of water = 3 km /hr = 3000 m/ hr Let d pipe take t hours to fill up the tank So, the volume of water that flows in t hours from the pipe = Area of cross section of pipe × speed × time = π = 30 π t m3 ∴ Volume of water that flows from the pipe into the tank in "t" hours = volume of the tank ⇒ 30 π t = 50 π ⇒ 30 t = 50 t = = = 1 hr 40 min = 100 minutes [∴ 1 hour = 60 minutes].
  • -5
Time=VOL.of cylinder /vol of pipe 
  • -4
The tank can be filled in 1 hour 36 mins and the cost of water is RS. 19.80. Follow the steps as taken by Indhumathi...bcoz I'm not able to post my answer.
  • -4
Diameter of pipe =2.5
  • -2

R = radius of cylinder = 6m

H = height of cylinder = 2.5m

r = radius of pipe = 25/2cm =1/8m

Rate of flow of water = 3.6km/hr

In 1 hr water upto a length of 3.6km = 3600m will come out of pipe.

let the tank be filled in 'x' hrs.

volume of water coming out of pipe in x hrs = volume of cylindrical tank.

(22/7)(1/8)(1/8)(3600)(x) = (22/7)(6)(6)(2.5)

          (1/8)(1/8)(3600)( x) = 6 x 6 x 2.5

                             3600(x) = 36 x 2.5 x 8 x 8

                                100(x) = 8 x 8 x 2.5

                               1000(x) = 8 x 8 x 25

                                         x = 16/10 = 1.6 hrs

                                        x = 1 hr.36 min.

Now,

            cost of water = volume of cylindrical tank x 0.07

                                   = 22/7 x 6 x 6 x 2.5 x 0.07

                                   = Rs.19.80.




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