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 ?

72

We have,

Volume of cube having side 'a' is given by V = a³

Sum of its side or edges = 12a

Total surface area A = 6a²

Let, each side of cube = a

Hence, sum of its all side = 12a

and volume V = a³

According to question, volume of cube = sum of its edges. Therefore

a³ = 12a

⇒ a(a² - 12) = 0,  a ≠ 0

⇒ a² = 12       -----(1)

Hence, the total surface area

A = 6a²

⇒ A = 6 × 12 = 72