A hollow hemisphere and a cone have equal bases. If their are also equal, then the ratio of their curved surface area will be:

This is a question from the previous CUET; it is wrong.

The question can be, "A hollow hemisphere and a cone have equal bases. If their heights are also equal, then the ratio of their curved surface area will be:"

If this is the question, then the answer will be as follows:

The curved surface area semi-sphere is $$2\pi\ r^2$$, that of a cone is $$\pi\ r\cdot\sqrt{\ r^2+h^2}$$.

Here r=h

$$\pi\ r\cdot\sqrt{\ r^2+r^2}=\pi\ r\cdot\sqrt{\ 2r^2^{ }}=\sqrt{\ 2}\pi\ r^2$$

$$2\pi\ r^2$$$$:\ \sqrt{\ 2}\pi\ r^2$$=$$\sqrt{\ 2}:1$$