The volume of a right circular cone, whose radius of the base is half of its altitude, and the volume of a hemisphere are equal. The ratio of the radius of the cone to the radius of the hemisphere is:

Volume of cone(V) =

$$\frac{1}{3} \pi r^2 h$$

Where,   r is the radius of cone

              h is the altitude

radius of the base is half of its altitude

                           $$r=\frac{h}{2}$$

                           $$h=2r$$

       $$V=\frac{1}{3}\pi r^{2}\times2r$$

                           V=$$\frac{2}{3}\pi r^{3}$$

Volume of the hemisphere, U = $$\frac {2}{3} \pi a^{3}$$

Where,a is the radius of hemisphere.

Given V=U

$$\frac {2}{3} \pi r^{3} $$ = $$\frac {2}{3} \pi a^{3} $$

=> $$r^{3} = a^{3}$$

Hence,       r=a

So,  $$\frac{r}{a}=1$$

r:a=1 : 1