CDS 2026 (I) Elementary Mathematics, question 61

Topic: Mensuration

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Q61

The diameter of a copper solid sphere is 66 cm. The sphere is melted and recast into a wire. If the diameter of the wire is 0.50.5 cm, then what is the length of the wire ?

  1. (a) 5.245.24 m
  2. (b) 5.365.36 m
  3. (c) 5.765.76 mCorrect answer
  4. (d) 5.965.96 m

Solution.

Answer: (c) 5.765.76 m

  1. Conserve copper volume.
  2. The sphere radius is 3 cm and the wire radius is 0.25 cm, so (4/3)π(3)3=π(0.25)2L(4/3)\pi(3)^{3} = \pi(0.25)^{2}L.
  3. Thus L=36/0.0625=576cm=5.76mL = 36/0.0625 = 576cm = 5.76m.
  4. 76 m.
  5. Use radii consistently; the stated dimensions are diameters.