Question : Three cubes of equal volume are joined end to end. Find the surface area of the resulting cuboid if the diagonal of the cube is $6 \sqrt{3} \mathrm{~cm}$.
Option 1: 509 cm2
Option 2: 504 cm2
Option 3: 516 cm2
Option 4: 512 cm2
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Correct Answer: 504 cm 2
Solution :
Diagonal of cube = $\sqrt{3}$ × side
⇒ $6\sqrt{3}$ = Side × $\sqrt{3}$
⇒ Side = 6 cm
So, length of cuboid, l = 3 × 6 = 18 cm
Breadth, b = 6 cm and height, h= 6 cm
So, the surface area of the cuboid
= 2(lb + bh + lh)
= 2(18 × 6 + 6 × 6 + 18 × 6)
= 2(108 + 36 + 108)
= 2 × 252 cm
2
= 504 cm
2
Hence, the correct answer is 504 cm
2
.
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