Q. 94.1( 9 Votes )
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
As the volume remains same when a body is recast to another body.
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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