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.

Answer 1

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.