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

In this question diameter of a metallic sphere is given. The sphere is melted and drawn into a wire of uniform cross-section. If the length of the wire is also given then find its radius.

This is the Question Number 01, Exercise 17.5 of M.L Aggarwal.

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# The diameter of a metallic sphere is 6 cm. The sphere is melted and drawn into a wire of uniform cross-section. If the length of the wire is 36 m, find its radius.

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Given diameter of the metallic sphere = 6 cm

Radius of the sphere, r = 6/2 = 3 cm

Volume of the sphere, V = (4/3)r

^{3}= (4/3)Ã—Ã—3

^{3}= 4Ã—Ã—9

= 36 cm

^{3}Length of the wire, h = 36 m = 3600 cm

Since the sphere is melted and drawn into a wire, volume remains the same.

Volume of the wire, r

^{2}h = 36r

^{2}Ã—3600 = 36r

^{2}Â = 1/100r = 1/10 = 0.1 cm = 1 mm

Hence the radius of the wire is 1 mm.