Given that,
Volumes are in the ration 1: 27
Therefore,
\(\frac{Volume1}{Volume2}=\frac{1}{27}=\frac{a^3}{b^3}\)
a = \(\frac{b}{\sqrt[3]27}\)
a = \(\frac{b}{3}\)
Or b = 3a
Or \(\frac{b}{a}=3\)
We have to find out ratio of their surface areas:
\(\frac{Surface\,area\,1}{Surface\,area\,2}=\frac{6a^2}{6b^2}\)
= \(\frac{a^2}{b^2}\)
= \(\frac{(\frac{b}{3}^2)}{b^2}\)
= \(\frac{1}{9}\)
Therefore, the surface areas are in the ratio 1: 9
Hence, option B is correct
