Let radius of sphere = $$R$$ cm Height of cone = $$h=40$$cm and radius of cone = $$r=30$$ cm => Slant height of cone = $$l=sqrt{h^2+r^2}$$ => $$l=sqrt{(40)^2+(30)^2}=sqrt{1600+900}$$ => $$l=sqrt{2500}=50$$ m Curved surface area of sphere = Curved surface area of cone => $$4pi R^2=pi rl$$ => $$4(r)^2=30 imes 50$$ => $$(r)^2 = frac{1500}{4}=375$$ => $$r=sqrt{375}=5sqrt{15}$$ cm => Ans - (C)