The length of a diagonal of a cube is \(5\sqrt{3}\) cm. The volume and the surface area of the cube are respectively:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 125 cm3 and 150 cm2
A cube of edge \(a\) has a diagonal of \(a\sqrt{3}\), so the given diagonal gives the edge first.
\(a\sqrt{3}=5\sqrt{3}\), so \(a=5\) cm
Volume \(=a^3=5^3=125\) cm3
Surface area \(=6a^2=6\times25=150\) cm2
Tip: Option (1) has the same two numbers in the wrong places. Volume is in cm3 and area in cm2, so match each number with its own unit.