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

(5/100)²**x** 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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