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Question

Water flows at the rate of 10m/minute through a cylindrical pipe 5mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40cm and depth 24cm?


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Solution

Step 1: Writing the given information

Base Diameter of conical pipe=40cm

Height of conical pipe, h=24cm

Base diameter of cylindrical pipe=5mm=0.5cm[Since1cm=10mm]

Rate of flow of water is height of cylinder i.e. 10m/minute=1000cm/minute.

Step 2: Finding the volume of conical vessel

Volumeofcone=13πr2h=13π(20)2(24)=3200πcm3

In cylindrical pipe,

Let t be the time taken to fill the conical vessel.

Water covers 10tm=1000tcm distance in pipe,

Step 3: Finding the volume of cylindrical pipe

Volumeofwaterpassedinpipe=Volumeofacylinder=πr2h=π(0.25)2(1000t)=62.5cm3

Step 4: Finding the time taken to fill a conical vessel from cylindrical pipe

Volumeofconicalvessel=Volumeofwaterthatpassesthroughpipeintminutes62.5=3200π62.5t=3200t=51.2minutes

We know that,

0.2minutes=0.2(60)seconds=12seconds[Since1minute=60seconds]

Therefore, t=51minutes12seconds

Therefore, the time taken to fill a conical vessel from cylindrical pipe, t=51minutes12seconds


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