Multiple choice

If the sphere of radius 6 cm is melted and drawn into a wire of radius 0.2 cm, then the length of the wire is

  1. 75 m

  2. 72 cm

  3. 72 m

  4. 75 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of sphere = 4/3 * pi * 6^3 = 4/3 * pi * 216 = 288 * pi. Volume of wire = pi * r^2 * h = pi * (0.2)^2 * h = 0.04 * pi * h. 288 * pi = 0.04 * pi * h. h = 288 / 0.04 = 7200 cm = 72 m.

AI explanation

By equating volumes, the volume of the sphere equals the volume of the cylindrical wire, using the formulas (4/3) * pi * R^3 and pi * r^2 * h. Substituting R = 6 cm and r = 0.2 cm gives (4/3) * pi * 6^3 = pi * 0.2^2 * h. Solving for h yields 288 / 0.04, which equals 7200 cm or 72 m.

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