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.