Question

A solid iron rectangular block of dimensions 4.4 m $\times$ 2.6 m $\times$ 1 m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.

Answer 1

Given that:

Internal radius $r=30$ cm
Thickness $w=5$ cm
External radius $R=30+5=35$ cm

Let the length of pipe be $h$.

Here,

The volume of cuboid $=$ Volume of a hollow cylinder

$440\times 260\times 100=\pi (R^2–r^2)h$

$\Rightarrow 440\times 260\times 100=\pi ({35}^2–{30}^2)h$

$\Rightarrow 440\times 260\times 100=\pi \left(325\right)h$

$\Rightarrow h=11204$

The length of the pipe $h=11204cm=112.04m$