Combination of Solids Solution10





In this page combination of solids solution10 we are going to see solution some practice questions of the worksheet combination of solid worksheet2.

Question 10:

Water in a cylindrical tank of diameter 4 m and height 10 m is released through a cylindrical pipe of diameter 10 cm at the rate of 2.5 km/hr. How much time will it take to empty the half of  the tank? Assume that the tank is full of water to begin with.

Solution:

Now we are going to convert every measurements into m

Diameter of the cylindrical tank = 4 m

radius of the cylindrical tank = 2 m

height of the tank = 10 m

Diameter of the cylindrical pipe = 10 cm

radius of the cylindrical pipe = 10/2 = 5 cm

                                                   = 5/100 m

speed of water = 2.5 km/hr

    1000 m = 1 km

                = 2.5 x 1000

                = 2500 m/hr

Volume of water discharged from

                   the cylindrical pipe = (1/2) Volume of cylindrical tank

Area of cross section x time x speed  = (1/2) Π r² h

                         Π r²x time x speed  = (1/2) Π r² h

             (5/100)²x time x 2500  = (1/2) (2)² (10)

(5/100) x (5/100) x time  x 2500  = (1/2) x (2) x 2 x (10)

                         Time = 2 x 10 x (100/5) x (100/5) x (1/2500)

                         Time = 80/25

                                = 3.2 hour

 1 hour = 60 minute

                               = 192 minute

                               = 180 + 12

3 hour and 12 minute     

Therefore time taken to empty the half of  the tank is 3 hour and 12 minute