This is the important question for cbse board exam. Given problem is the combination of two shape that is sphere and cylinder. To find answer of this question we need to use volume of sphere and volume of cylinder formulas. Problem number 18 from RS Aggarwal book exercise 17B, page number 810, chapter volume and surface area of solid.

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# The diameter of a copper sphere is 18 cm. It is melted and drawn into a long wire of uniform cross-section. If the length of the wire is 108 m, find its diameter

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Solution

given data,

Diameter of sphere = 18 cm

Radius of the sphere = 9 cm

Volume of sphere = [4/3] πr³

= [4/3] π × 9³ cm³

Length of wire = 108 m = 10800 cm

radius of the wire = r cm.

Volume of the wire = πr²l

= πr²×10800 cm³

volume of the sphere = volume of the wire

∴ [4/3] π × 9³ = πr²×1080

[4/3] × 9³ = r²×1080

([4/3] × 9³) / 1080 = r²

r² = 0.09

r = √0. 09

r = 0. 3 cm

dimeter = 2r = 2 ×0. 3 cm = 0. 6 cm

∴ The diameter of the wire is 0.6 cm.