Question

1. 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.
​

Answer 1

Answer:

Step-by-step explanation:

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

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