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.

Answer :

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.

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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