Question:
The length of the diagonal of a cube is $6 \sqrt{3} \mathrm{~cm}$. Its total surface area is
(a) 144 cm2
(b) 216 cm2
(c) 180 cm2
(d) 108 cm2
Solution:
(b) 216 cm2
Let the edge of the cube be a cm.
Then, length of the diagonal $=\sqrt{3} a$
Or,
$\sqrt{3} a=6 \sqrt{3}$
$\Rightarrow a=6 \mathrm{~cm}$
Therefore, the total surface area of the cube = 6a2
$=(6 \times 6 \times 6) \mathrm{cm}^{3}$
$=216 \mathrm{~cm}^{3}$
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