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Question 57

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. The height of the cone is

Solution

Internal and External radius of sphere are 2 cm and 4 cm respectively, and radius of cone = 4 cm.

Let height of cone = $$h$$ cm

Volume of hollow sphere = Volume of cone

=> $$\frac{4}{3}\pi\times[(r_1)^3-(r_2)^3]=\frac{1}{3}\pi R^2h$$

=> $$4\times(4^3-2^3)=(4)^2\times h$$

=> $$h=\frac{4\times56}{16}$$

=> $$h=14$$ cm

=> Ans - (B)

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