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?

15000 cm²

We know that,

Diagonal of cube = \(\sqrt {3}\) × Side of cube

The total surface area of cube = 6(side)²

We have,

Diagonal = 50\(\sqrt {3}\) cm.

According to the question, 

side\(\sqrt {3}\) = 50\(\sqrt {3}\)

side = 50

Now, Total surface area of cube = 6 ×(50)² = 15000cm²