The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire.
Answers
Given : Diameter of a sphere ,D = 6 cm.
Diameter of a wire ,d = 0.2 cm.
Radius of a sphere, R = D/2 = 6/2 = 3 cm
Radius of a wire, r = d/2 = 0.2/2 = 0.1 cm
Let the length of the wire be h cm.
Volume of material in the wire = Volume of the sphere of radius 6 cm
πr²h = 4/3πR³
⇒ r²h = 4/3 R³
⇒ 0.1² × h = 4/3 × 3³
⇒ 0.01 × h = 4 × 9
⇒ h = 36/0.01
⇒ h = 36 × 100
⇒ h = 3600 cm
⇒ h = 36 m
[1cm = 1/100 m]
Hence, the length of the wire is 3600 cm or 36 m .
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Answer:⇒ r²h = 4/3 R³
⇒ 0.1² × h = 4/3 × 3³
⇒ 0.01 × h = 4 × 9
⇒ h = 36/0.01
⇒ h = 36 × 100
⇒ h = 3600 cm
⇒ h = 36 m
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