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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