The diameter of a copper sphere is 18 cm .It is melted and drawn into a long wire of uniform section .If the length of the wire is 108 m , find its diameter .
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Answer:
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Step-by-step explanation:
Given,
Diameter of copper sphere D=18 cm
Length of wire l=108 m=10800 cm
Hence,
Radius of copper sphere R=
2
D
=9 cm
Volume of copper sphere V=
3
4
πR
3
=
3
4
π(9)
3
cm
3
=
3
4
×π×729 cm
3
=972 π cm
3
The sphere is melted and is drawn in a wire (cylindrical) of radius (r) and hight 108 m.
→Volume of sphere = Volume of wire
Volume of wire V=πr
2
l
972π cm
3
=πr
2
×10800 cm
r
2
=
10800
972
cm
2
r
2
=0.09 cm
2
r=0.3 cm
Hence,
Diameter of the wire d=2r=0.6 cm