Question : There is a wooden sphere of radius $6 \sqrt{3}$ cm. The surface area of the largest possible cube cut out from the sphere will be:
Option 1: $864$ cm2
Option 2: $464 \sqrt{3}$ cm2
Option 3: $462$ cm2
Option 4: $646\sqrt{3}$ cm2
Correct Answer: $864$ cm 2
Solution :
Given: Radius of the sphere, $r= 6\sqrt3$
Diagonal of the cube = diameter of sphere $=2×r=2×6\sqrt3=12\sqrt3$
We know that,
Edge of the cube, $a= \frac{\text{Diagonal length}}{\sqrt3}=\frac{12\sqrt3}{\sqrt3} = 12$
$\therefore$ Total surface area of the cube $=6a^2=6×12^2= 864$
Hence, the correct answer is $864$ cm
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