question_answer

The dimensions of a solid iron cuboid are \[4.4\text{ }m\times 2.6\text{ }m\times 1.0\text{ }m\]. 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.

Answer:

Inner radius of pipe \['r'=30\text{ }cm\]

Thickness of pipe \[=5\text{ }cm\]

\[\therefore \]      Outer radius \[=30+5\]

\[\Rightarrow \]                    \[R=35\,\,cm\]

Now,           Vol. of hollow pipe = Vol. of cuboid

\[\pi h\left( {{R}^{2}}-{{r}^{2}} \right)=l\times b\times h\]

\[\frac{22}{7}\times h[{{35}^{2}}-{{30}^{2}}]=4.4\times 2.6\times 1\times 100\times 100\times 100\]

\[\frac{22}{7}\times h\times 65\times 5=44\times 26\times 1\times 100\times 100\]

\[h=\frac{44\times 26\times 100\times 100\times 7}{22\times 65\times 5}\]

\[=11200\,\,cm\]

\[=112\,\,m\]