A sphere has the same curved surface area as a cone of vertical height 40 cm and radius 30 cm. The radius of the sphere is
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
=> $$4\pi R^2=\pi rl$$
=> $$4(r)^2=30 \times 50$$
=> $$(r)^2 = \frac{1500}{4}=375$$
=> $$r=\sqrt{375}=5\sqrt{15}$$ cm
=> Ans - (C)
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