SSC Sample Paper Mock Test-10 SSC CGL Tear-II Paper-1

The length, breadth and height of a rectangular parallelepiped are in ratio 6:3:1. If the surface area of a cube is equal to the surface area of this parallelepiped, then what is the ratio of the volume of the cube to the volume of the parallelepiped?

A) 1 : 1

B) 5 : 4

C) 7 : 5

D) 3 : 2

Correct Answer: D

Solution :

Let the length, breadth and height of a rectangular parallelepiped be 6x, 3x and x.

Also, let the side of a cube be a.

By given condition,

Surface area of a Cube = Surface area of rectangular parallelepiped

\[6\,\,{{(a)}^{2}}=2\,\,(6x\times 3x+3x\times x+x\times 6x)\]

\[\Rightarrow \]\[6{{a}^{2}}=2\,\,(18{{x}^{2}}+3{{x}^{2}}+6{{x}^{2}})\]\[\Rightarrow \]\[6{{a}^{2}}=54{{x}^{2}}\]

\[\therefore \] \[a=3x\]

Now, \[\frac{\text{Volume}\,\,\text{of}\,\,\text{cube}}{\text{Volume}\,\,\text{of}\,\,\text{rectangle}\,\,\text{paralleopiped}}\]

\[=\frac{{{a}^{3}}}{6x\times 3x\times x}=\frac{{{(3x)}^{3}}}{18{{x}^{3}}}=\frac{27}{18}=\frac{3}{2}\]