A solid is hemispherical at the bottom and conical above.

Solution:

Let r be the radius of the base and h be the height of conical part.

Since,

Surface area of both part of solid is equal.

i.e.,

$l=2 r$      ..............$(i)$

But,

$I=\sqrt{h^{2}+r^{2}}$

Squaring on both side,

Then we get,

$l^{2}=h^{2}+r^{2}$

From equation (i) putting the value of l in above equation

$4 r^{2}=h^{2}+r^{2}$

$3 r^{2}=h^{2}$

$\frac{r}{h}=\frac{1}{\sqrt{3}}$

$r: h=1: \sqrt{3}$

Hence, the correct answer is choice (b).