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  4. The volume of a cube in m3 is equal to the surface area of the cube in m2. The volume of the cube is

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Q. The volume of a cube in $ m^3 $ is equal to the surface area of the cube in $m^2$. The volume of the cube is

Delhi UMET/DPMTDelhi UMET/DPMT 2006Physical World, Units and Measurements

Solution:

Let length of side of the cube be a then volume of cube = $a^3$
Also, surface area of cube = 6 $a^2$
Given, volume of cube = surface area of cube
or $ a^3 = 6a^2 $
$\Rightarrow a = 6 $ m
Thus, volume of the cube = $( 6 )^3 = 216 \,m^3$