Question

A solid in hemisphere at the bottom and conical above. If the surface are of the part our equal, find the ratio of radius and height of conical part.

Answer 1

We have,

Surface area of Hemisphere=Surface Area of Cone

Let the radius of hemisphere $=r$

And let the slant length of Cone$=l$

But according to given question,

$2\pi r^2=\pi rl$

$\Rightarrow 2r=l$

We know that,

In cone,

$h=\sqrt{l^2-r^2}$

$\Rightarrow h=\sqrt{4r^2-r^2}$

$\Rightarrow h=\sqrt{3}r$

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

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

Or

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

Hence, this is the answer.