How Much Radius of Wire in an Iron Sphere ?

An iron sphere of radius 27 cm is melted to from a wire of length 729 cm. The radius of wire is

  1. 6 cm
  2. 9 cm
  3. 18 cm
  4. 36 cm
Abdul Salam Newbie Asked on 5th September 2015 in Maths.
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1 Answer(s)

Answer: (1) 6 cm
Explanation:-
The radius of an iron sphere = 27 cm
Formula-
The volume of an iron sphere = 4 x pai x r3/3
Where, r = the radius of a sphere.
Then, the volume of a sphere = 4 x 22 x 273/7 x 3cm3
Formula-
The volume of the wire = pai x r2 x h
where, r = radius of the wire & h = the length of the wire.
Then, the volume of the wire = 4 x 22 x 273/7 x 3 = pai x r2 x 729
4 x 22 x 27 x 27 x 27/7 x 3 = 22 x r2 x 729/7
4 x 9 x 27 x 27 = r2 x 729
4 x 9 = r2
36 = r2
r = 6 cm              (square root of both side)
Hence, the radius of the wire is 6 cm.

Anurag Mishra Professor Answered on 6th September 2015.
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