The volume of first sphere = 27 x volume of second sphere
Let the radius of the first sphere = r1 and, radius of second sphere = r2
(i) Then, according to the question we have
\[\begin{array}{*{35}{l}}
4/3\text{ }\pi {{r}_{1}}^{3}~=\text{ }27\text{ }\left( 4/3\text{ }\pi {{r}_{2}}^{3} \right) \\
{{r}_{1}}^{3}/\text{ }{{r}_{2}}^{3}~=\text{ }27 \\
{{r}_{1}}/\text{ }{{r}_{2}}~=\text{ }3/\text{ }1 \\
Thus,\text{ }{{r}_{1}}:\text{ }{{r}_{2~}}=\text{ }3:\text{ }1 \\
\end{array}\]
(ii) Surface area of the first sphere = 4 πr12
And the surface area of second sphere = 4 πr22
Ratio of their surface areas
\[=\text{ }4\text{ }\pi {{r}_{1}}^{2}/\text{ }4\text{ }\pi {{r}_{2}}^{2}~=\text{ }{{r}_{1}}^{2}/\text{ }{{r}_{2}}^{2}~=\text{ }{{3}^{2}}/\text{ }{{1}^{2}}~=\text{ }9\]
Hence, the ratio = 9: 1