(b) 1 : 2
Let each side of the base of the original prism be a units and the height of the prism be h units. Then
Required ratio = \(\frac{\text{Vol. of original prism}}{\text{Vol. of new prism}}\)
= \(\frac{\frac{\sqrt3}{4}\times(a)^2\times{h}}{\frac{\sqrt3}{4}\times(2a)^2\times\frac{h}{2}}\) = \(\frac{2a^2h}{4a^2h}\) = 1 : 2.