Multiple choice

A solid copper sphere of radius 9 cm is melted and reformed into a wire of radius 1 mm. What will be the length of this wire? (Take π = 22/7)

  1. 1166.4 metres

  2. 1458 metres

  3. 777.6 metres

  4. 972 metres
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of sphere = 4/3 * pi * 9^3 = 4/3 * pi * 729 = 972 * pi. Volume of wire = pi * r^2 * h = pi * (0.1 cm)^2 * h = pi * 0.01 * h. 972 * pi = 0.01 * pi * h. h = 97200 cm = 972 meters.

AI explanation

The volume of the copper sphere is preserved when it is drawn into a wire, meaning the volume of the sphere equals the volume of the cylindrical wire. Using the sphere volume formula, the original volume is 4 thirds pi times 9 cubed, which equals 972 pi cubic centimeters. The wire has a radius of 1 millimeter, which is 0.1 centimeters, so its cross sectional area is 0.01 pi square centimeters. Setting the volumes equal gives 972 pi equals 0.01 pi times the length, so the length is 97200 centimeters, or 972 metres.

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