If the longest diagonal of a cube is \(6\sqrt{3}\) cm, then its volume and surface area are _____ and _____ respectively.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 216 cm3 and 216 cm2
The longest diagonal of a cube runs from one corner to the opposite corner through the inside. For a cube of side \(a\), the diagonal of a face is \(a\sqrt{2}\), and with the edge \(a\) at right angles to it the longest diagonal is \(\sqrt{2a^2+a^2}=a\sqrt{3}\).
Finding the side: \(a\sqrt{3}=6\sqrt{3}\), so \(a=6\) cm
Volume of the cube: \(a^3=6^3=216\) cm3
Surface area, six square faces: \(6a^2=6\times36=216\) cm2