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Home » A metal pipe has a bore (inner diameter) of 5 cm. The pipe is 5 mm thick all round. Find the weight, in kilogram, of 2 metres of the pipe if 1 cm3 of the metal weights 7.7 g.
A metal pipe has a bore (inner diameter) of 5 cm. The pipe is 5 mm thick all round. Find the weight, in kilogram, of 2 metres of the pipe if 1 cm3 of the metal weights 7.7 g.
Class 10 | Cylinder, Cone and Sphere (Surface Area and Volume) | Exercise 20A | ICSE | Selina
A metal pipe has a bore (inner diameter) of 5 cm. The pipe is 5 mm thick all round. Find the weight, in kilogram, of 2 metres of the pipe if 1 cm3 of the metal weights 7.7 g.

Inner radius of the pipe = r = 5/2 = 2.5 cm

External radius of the pipe = R = Inner radius of the pipe + Thickness of the pipe

    \[=\text{ }2.5\text{ }cm\text{ }+\text{ }0.5\text{ }cm\text{ }=\text{ }3\text{ }cm\]

Length of the pipe = h = 2m = 200 cm

Volume of the pipe = External Volume – Internal Volume

    \[\begin{array}{*{35}{l}} =\text{ }\pi {{R}^{2}}h\text{ }-\text{ }\pi {{r}^{2}}h \\ =\text{ }\pi \left( {{R}^{2}}~-\text{ }{{r}^{2}} \right)h \\ =\text{ }\pi \text{ }\left( R\text{ }+\text{ }r \right)\left( R\text{ }-\text{ }r \right)\text{ }h \\ =\text{ }22/7\text{ }\left( 3\text{ }-\text{ }2.5 \right)\left( 3\text{ }+\text{ }2.5 \right)\text{ x }200 \\ =\text{ }22/7\text{ }\left( 0.5 \right)\text{ }\left( 5.5 \right)\text{ x }200\text{ }=\text{ }1728.6\text{ }c{{m}^{3}} \\ \end{array}\]

Since, 1 cm3 of the metal weight 7.7g,

Hence, weight of the pipe

    \[=\text{ }\left( 1728.6\text{ }x\text{ }7.7 \right)g\text{ }=\text{ }\left( 1728.6\text{ }x\text{ }7.7 \right)/\text{ }1000\text{ }kg\text{ }=\text{ }13.31\text{ }kg\]

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