(d) 3 : 2
Let the length, breadth and height of the rectangular parallelopiped be 6\(x\), 3\(x\) and \(x\).
Let the side of the cube be a.
∴ By the given condition,
Surface area of a cube
= Surface area of rectangular parallelopiped
6(a)2 = 2(6\(x\) x 3\(x\) + 3\(x\) x \(x\) + \(x\) x 6\(x\))
⇒ 6a2 = 2(18\(x\)2 + 3\(x\)2 + 6\(x\)2)
⇒ 6a2 = 54\(x\)2 ⇒ a2 = 9\(x\)2
⇒ a = 3\(x\)
Now, Volume of cube : Volume of rectangular parallelopiped
= a3 : (6\(x\) x 3\(x\) x \(x\)) = (3\(x\))3 : 18\(x\)3 = 27 : 18 = 3 : 2.