ICSE Board Question Based on Mensuration Chapter of M.L Aggarwal for class10

In this question,

A hollow sphere of internal and external diameters are given, is melted into a cone of given base diameter .

You have to find the height of the cone.

This is the Question Number 13, Exercise 17.5 of M.L Aggarwal.

Deepak BoraNewbie

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

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Given internal diameter of hollow sphere = 4 cmInternal radius, r = 4/2 = 2 cmExternal diameter = 8 cmExternal radius, R = 8/2 = 4 cmVolume of the hollow sphere, V = (4/3)(R^{3}-r^{3})V = (4/3)Ã—(4^{3}-2^{3})V = (4/3)Ã—(64-8)V = (4/3)Ã—56Base diameter of the cone = 8 cmRadius, r = 8/2 = 4 cmVolume of cone = (1/3)r^{2}h= (1/3)Ã—4^{2Â }Ã—h= (16/3)Ã—hSince sphere is melted and changed into a cone, their volumes remain same.

(4/3)Ã—56 = (16/3)Ã—hh = 4Ã—56/16h = 14 cmHence the height of the cone is 14 cm.