The volume of a cube is numerically equal to the sum of the lengths of all its edges. What is its total surface area in sq. units?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 72
A cube of edge \(a\) has 12 equal edges, volume \(a^3\) and total surface area \(6a^2\). Setting the volume equal to the total edge length gives \(a\).
\(a^3=12a\)
\(a^2=12\) (an edge cannot be zero)
Total surface area \(=6a^2=6\times12=72\) sq. units
There is no need to find \(a=2\sqrt{3}\) itself: the surface area needs only \(a^2\).