Math, asked by Soudha, 1 year ago

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

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Answers

Answered by InesWalston
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

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