| If two adjacent sides of a rectangular parallelepiped are 1 cm and 2 cm and the total surface area of the parallelepiped is \[22\,\,c{{m}^{2}},\]then the diagonal of the parallelepiped is [SSC (10+2) 2012] |
A) \[\sqrt{10}\,\,cm\]
B) \[2\sqrt{3}\,\,cm\]
C) \[\sqrt{14}\,\,cm\]
D) \[4\,\,cm\]
Correct Answer: C
Solution :
| Let the third side of the rectangular parallelepiped be x. |
| Total surface area of parallelepiped \[=22\] |
| \[\Rightarrow \] \[2\,\,(lb+bh+lh)=22\] |
| \[\Rightarrow \]\[2\,\,(x\times 1+1\times 2+2\times x)=22\] |
| \[\Rightarrow \] \[3x+2=11\] |
| \[\Rightarrow \] \[3x=11-2=9\] |
| \[\Rightarrow \] \[x=\frac{9}{3}=3\,\,cm\] |
| \[\therefore \]Diagonal of parallelepiped\[=\sqrt{{{l}^{2}}+{{b}^{2}}+{{h}^{2}}}\] |
| \[=\sqrt{{{3}^{2}}+{{2}^{2}}+{{1}^{2}}}\] |
| \[=\sqrt{9+4+1}=\sqrt{14}\,\,cm\] |
You need to login to perform this action.
You will be redirected in
3 sec
