. Water flows at the rate of 10 m per minute through


a cylindrical pipe having its diameter as 5 mm. How much time will it take to fill a conical vessel whose diameter of base is 40 cm and depth 24 cm.

Best Answer

Explanation:
Given, water flows at the rate of 10m/min through a cylindrical pipe of 5 in diameter.
A conical vessel has a diameter at base 40cm and depth 24cm.
Let’s find the time required to fill the conical vessel.
Volume of cylinder =πr2h
Given, diameter =5mm
Radius 5/2 =2.5mm
1cm =100cm
So, r=2.5/10=0.25cm
Rate of flow =10m/min
1m =100cm
So, rate of flow =10(100)cm/min
Volume of water that flows out in 1 minute =π (0.25) 2(10) (100)
=62.5πcm3
Volume of conical vessel =(1/3) πr2h
Given, diameter =40cm 
Radius =40/2=20cm
Depth h=24cm
=(1/3)π(20) 2(24)
=400π(8)
3200πcm3
Given, time required to fill the vessel = volume of conical vessel/volume of water that flows out of cylindrical pipe in one minute
=3200π/62.5π
=3200/62.5
=51.2 minutes.
Final Answer:
Hence, filling the conical vessel takes 51.2 minutes.

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