| If \[1\,\,c{{m}^{3}}\] of a metal weight 28 g, then the weight of a pipe of length 2 m with a bore 5 cm and in which the thickness of the metal is 1 cm, is |
A) 105.6 kg
B) 50.8 kg
C) 115.4 kg
D) 45.4 kg
Correct Answer: A
Solution :
| External radius \[=3.5\,\,cm\] |
| Length \[=200\,\,cm\] |
| Internal radius \[=2.5\,\,cm,\]Length \[=200\,\,cm\] |
| External volume \[=[\pi \times {{(3.5)}^{2}}\times 200]\,\,cm\] |
| Internal volume \[=[\pi \times {{(2.5)}^{2}}\times 200]\,\,cm\] |
| Volume of metal |
| \[=[\pi \times {{(3.5)}^{2}}\times 200-\pi \times {{(2.5)}^{2}}\times 200]\] |
| \[=\pi \times 200\times [{{(3.5)}^{2}}-{{(2.5)}^{2}}]\] |
| \[=\frac{22}{7}\times 200\times 6\times 1\,\,cm\] |
| Weight of the metal |
| \[=\frac{22\times 200\times 6\times 28}{7\times 1000}=105.6\,\,kg\] |
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