If the volume of a cube is given as 12167cm
3
, then the surface area of the cube will be:

Let the edge length of the cube be acm.
The formula for the volume (V) of a cube is:

V=a
3

Given that V=12167cm
3
:

a
3
=12167
a=
3

12167

​
=23cm
(Since 20
3
=8000 and 30
3
=27000, and the last digit is 7, the number must be 23).

The formula for the total surface area (TSA) of a cube is:

TSA=6a
2

Substitute the value of a=23:

TSA=6×(23)
2

TSA=6×529=3174cm
2