A solid iron cuboidal block of dimensions is recast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.


For cuboidal block


Length, l = 4 m


Breadth, b = 2.6 m


Height, h = 1 m


We know that,


Volume of tank = lbh


Where, l, b and h are the length, breadth and height of tank respectively


Volume of cuboid = 4.4(2.6)(1) = 11.44 m3


Also,


As the volume remains same when a body is recast to another body.


We have


Volume of cylindrical pipe = 11.44 m3


Now, For pipe,[i.e. hollow cylinder]


Internal radius, r2 = 30 cm = 0.3 m


Thickness = 5 cm


External radius, r1 = Internal radius + thickness = 30 + 5 = 35 cm = 0.35 m


Let the length of pipe be h


Also, we know


Volume of a hollow cylinder = πh(r12 - r22), as shown below:



Where h is height and r1 and r2 are external and internal diameters respectively.


So, we have


Volume of pipe = πh((0.35)2 - (0.3)2)




So, the length of pipe is 112 m.


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