Question : The length of the longest diagonal that can be placed in a closed cube is $50 \sqrt{3}$ cm. What is the total surface area of this cube?
Option 1: 15000 cm2
Option 2: 10000 cm2
Option 3: 12000 cm2
Option 4: 6000 cm2
Correct Answer: 15000 cm 2
Solution :
Let $a$ be the side of the cube.
The length of the longest diagonal that can be placed in a closed cube = $50 \sqrt{3}$ cm
$⇒\sqrt3 a=50 \sqrt{3}$
$\therefore a = 50$ cm
Total surface area = $6a^2= 6 × 50 × 50= 15000$ cm
2
Hence, the correct answer is 15000 cm
2
.
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