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
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