Total surface area of the cube = 150 $\text{ cm}^2$

Directly find the side length using $a = \sqrt{\frac{\text{TSA}}{6}}$ and cube it to get the volume in under 15 seconds.

Confusing total surface area with curved or lateral surface area ($4a^2$ instead of $6a^2$) or forgetting to cube the side length for volume.

Questions involving scaling of dimensions in mensuration can often be solved quickly using ratio properties of surface area ($a^2$) and volume ($a^3$).