The square of the diagonal of a cube is 2346 cm
2
. What is the total surface area (in cm
2
) of the cube?

Let the side length of the cube be a.
The formula for the diagonal (d) of a cube is:

d=
3

​
a
The square of the diagonal is given as 2346 cm
2
:

d
2
=(
3

​
a)
2
=3a
2

3a
2
=2346
a
2
=
3
2346
​
=782
The formula for the total surface area (TSA) of a cube is:

TSA=6a
2

Substitute the value of a
2
:

TSA=6×782=4692 cm
2