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Question

A solid iron cuboidal block of dimensions 4.4m,2.6m,1m is cast into a hollow cylindrical pipe of internal radius 30cmand thickness 5cm.. Find length of the pipe.


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Solution

Step 1: Find the volume of cylindrical pipe

Dimensions of cuboidal block

Length (l)=4m

Breadth (b)=2.6m

Height (h)=1m

Dimensions of cylindrical pipe:

Internal radius r2 =30cm =0.3m

Thickness=5cm=0.05m

So the outer radius r1 =30+5cm=35cm=0.35m

Let the length of the pipe =hmetre

We know, the volume of a hollow cylinder =πhr12-r22,

where π=227,r1=externalradius,r2=internalradius

We know, when a shape is recast into a different shape, then the volume stays the same.

Here, Cuboidal block is recast into cylindrical pipe. So, volume of the cuboidal block equals the volume of hollow cylinder.

We know, Volume of a cuboidal tank =l×b×h

=4.4×2.6×1m3=11.44m3

Then, Volume of cylindrical pipe will also be=11.44m3 [ Because the cuboidal tank is melt and recast into the cylindrical pipe]

Step 2: Find the height of the pipe

Also, we have volume of a hollow cylinder =πhr12-r22

So equating the above two, we get:

πhr12-r22=11.44

Now, putting the values of r1,r2,π in the equation above, we get:

11.44m3=227×h×(0.352-0.32)11.44=227×h×0.1225-0.0911.44=227×h×0.032511.44=0.7157×hh=11.44×70.715h=112m

Thus, the length of the pipe is 112m


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