The dimensions of a solid iron cuboid are $4.4\ m\times \ 2.6m\times 1.0\ m.$ It is melted and recast into a hollow cylindrical pipe of 30 cm inner radius and thickness 5 cm. Find the length of the pipe.

Given: A cuboid of the dimension $4.4\ m\times \ 2.6m\times 1.0\ m.$ radius of the pipe$=30\ cm$ and inner thickness$ =5\ cm$.

To do: To find the length of the pipe.

Solution:

Volume of cuboid $=4.4\ m\times \ 2.6m\times 1.0\ m.=11.44\ m^{2}$

Let us say length of the pipe$=l\ cm=\frac{l}{100} \ m$

Inner radius $=\ 30\ cm=\frac{30}{100}\ m$

Outer radius $=35\ cm=\frac{35}{100}\ m$

Volume of the cylindrical pipe$=\pi \left( r^{2}_{1} -r^{2}_{2}\right) l$

$=\pi \times \frac{1}{100\times 100}\left( 35^{2} -30^{2}\right) l\ m^{3}$

Volume of cuboid $=$ volume of cylindrical pipe

$11.44=\frac{\pi l}{100\times 100\times 100}\left( 35^{2} -30^{2}\right)$

$\Rightarrow l=\frac{11.44\times 100\times 100\times 100}{\pi \times 65\times 5}$

$\Rightarrow l=10.205\times 10^{4} \ m^{3}$

$\Rightarrow l=102.05\ km$

Thus the length of the pipe is $102.05\ km$.
 

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Updated on: 10-Oct-2022

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