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.
Deepak BoraNewbie
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)r3
= (4/3)××33
= 4××9
= 36 cm3
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, r2h = 36
r2×3600 = 36
r2 = 1/100
r = 1/10 = 0.1 cm = 1 mm
Hence the radius of the wire is 1 mm.