Question 70

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

Solution

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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