SSC Sample Paper Mock Test-20 SSC CGL Tear-II Paper-1

A hollow iron pipe is 21 cm long and its exterior diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs \[8\text{g}\,/\,\text{c}{{\text{m}}^{\text{2}}},\] then the weight of the pipe is \[\left( \text{Take}\,\,\pi =\frac{22}{7} \right)\]

A) 3.696 kg

B) 3.6 kg

C) 36 kg

D) 36.9 kg

Correct Answer: A

Solution :

The pipe can be assumed as hollow cylinder.

External radius \[=\frac{8}{2}=4\,\,\text{cm}\]Thickness \[=1\,\,\text{cm}\]

\[\therefore \] Internal radius \[=4-1=3\]

Volume of the material \[=\pi h\,\,({{R}^{2}}-{{r}^{2}})\]

\[=\frac{22}{7}\times 21\times \,\,({{4}^{2}}-{{3}^{2}})=\frac{22}{7}\times 21\times 7=462\,\,\text{c}{{\text{m}}^{\text{3}}}\]

Now, \[1\,\,\text{c}{{\text{m}}^{\text{3}}}\]iron weighs \[=8\,\,\text{g}\]

\[\therefore \]\[462\,\,\text{c}{{\text{m}}^{\text{3}}}\]iron weighs \[=462\times 8\,\,\text{g}=\frac{462\times 8}{1000}\,\,\text{kg}\]

\[=3.696\,\,\text{kg}\]