A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two

Question

A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres taken together, is :\

Professor PC Thomas Classes · Answer

(c): Let $r$ be the radius of the sphere.
 Since the sphere is cut into two hemispheres.\ So, the radius of each hemisphere will be same as that of sphere, i.e., r.\ Now, surface area of sphere $=4 \pi r^{2}$\ Surface area of two hemispheres $=2 	imes 3 \pi r^{2}=6 \pi r^{2}$\ $	herefore \quad$ Required ratio $=4 \pi r^{2}: 6 \pi r^{2}=2: 3$\ Concept Applied -Total surface area of hemisphere $=3 \pi r^{2}$