If the length of diagonal of a cube is

Question:

If the length of diagonal of a cube is $8 \sqrt{3} \mathrm{~cm}$, then its surface area is

(a) $192 \mathrm{~cm}^{2}$

(b) $384 \mathrm{~cm}^{2}$

(c) $512 \mathrm{~cm}^{2}$

(d) $768 \mathrm{~cm}^{2}$

 

Solution:

(b) $384 \mathrm{~cm}^{2}$

We have:

$\sqrt{3} a=8 \sqrt{3}$

$\Rightarrow a=8 \mathrm{~cm}$

$\therefore$ Surface area of the cube $=6 a^{2}=6 \times 8 \times 8=384 \mathrm{~cm}^{2}$

 

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