This question was asked in 2009 cbse board exam. Question from RS Aggarwal book chapter volume and surface area of solid, page number 811, exercise 17B, problem number 27
Deepak BoraNewbie
A farmer connects a pipe of internal diameter 25 cm from a canal into a cylindrical tank in his field, which is 12 m in diameter and 2.5 m deep. If water flows through the pipe at the rate of 3.6 km/hr, then in how much time will the tank be filled? Also, find the cost of water if the canal department charges at the rate of 0.07 per m³
Share
given data
the radius of the cylindrical tank, R = 12/2 = 6 m = 600 cm,
the depth of the tank, H = 2. 5 m = 250 cm,
the radius of the cylindrical pipe, r = 25/2 = 12. 5 cm
speed of the flowing water = 3.6km/hr
In 1 hr water up to 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.
πr²h = πR²H
(22/7) (1/8)² (3600) (x) = (22/7) (6)² (2.5)
(1/8)² (3600) (x) = (6)² (2.5)
x = [ (6)² (2.5) ] / [ (1/8)² (3600) ]
3600(x) = 36 *2.5 * 8
x = 16/10
x = 1.6 hrs
x = 1 hr.36 min.
Now,
cost of water = volume of cylindrical tank * 0.07
= πr²h * 0.07
= [22/7] * 6² * 2.5 * 0.07
= Rs.19.80.
∴The tank will be filled in 1hr.36 min and the cost of water will be Rs.19.80.