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Question
The radius of a metallic sphere is 8 cm. It was melted to make a wire of diameter 6 mm. Find the length of the wire.
Solution
The radius of a metallic sphere (r) = 8 cm
The diameter of a wire = 6 mm
∴ Its radius (r1) = 3 mm = `3/10` cm ......[∵ 1 cm = 10 mm]
Let h be the length.
Wire is created by melting a spherical.
∴ Volume of wire = Volume of sphere
∴ `πr_1^2h = 4/3 πr^3`
∴ `3/10 xx 3/10 xx h = 4/3 xx 8 xx 8 xx 8`
h = `(4 xx 8 xx 8 xx 8 xx 10 xx 10)/(3 xx 3 xx 3)`
h = `204800/27` = 7585.1851 cm
h = 75.85 m ......[∵ 1 m = 100 cm]
The length of the wire is 75.85 m.
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