Question

A hemisphere and a cone have equal bases. If their heights are also equal, then what is the ratio of their curved surfaces?

Answer 1

The base of the cone and hemisphere are equal. So radius of the two is also equal.

and

Height of the hemisphere = height of the cone

Then the slant height of the cone

Now, the curved surface area of

Hemisphere

and

The curved surface area of cone

Putting the value of l from eq. (i)

We get

Now,