Question

solve the questions...
but marking answer may not be correct..
plz help me...

Answer 1

Answer-

Volume of the cube is 64 cm³

Solution-

Let us assume that, the length of the side of the cube be x cm

Then, sum of length of all its sides is $12x$ cm

And the longest diagonal of the cube is $\sqrt3 x}$ cm

According to the question, the difference between one sixth of sum of length of all edges of the cube and longest diagonal is $\dfrac{4}{2+\sqrt3}$ cm, so

$\Rightarrow (\frac{1}{6}\times 12x)-\sqrt3x=\dfrac{4}{2+\sqrt3}$

$\Rightarrow 2x-\sqrt3x=\dfrac{4}{2+\sqrt3}$

$\Rightarrow (2-\sqrt3)x=\dfrac{4}{2+\sqrt3}$

$\Rightarrow x=\dfrac{4}{(2+\sqrt3)(2-\sqrt3)}=\dfrac{4}{(2)^2-(\sqrt3)^2}=\dfrac{4}{4-3}=\dfrac{4}{1}=4$

then volume of the cube is,

$=x^3=4^3=64\ cm^3$