Multiple choice

A copper sphere of radius 3 cm is beaten and drawn into a wire of diameter 0.2 cm. The length of the wire is

  1. 12

  2. 36

  3. 17

  4. 18

  5. 24
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The volume of the copper sphere (4/3 * pi * r^3) is equal to the volume of the cylindrical wire (pi * r_wire^2 * length). With r=3 and r_wire=0.1, the equation is 4/3 * pi * 27 = pi * 0.01 * L. Solving for L gives 3600 cm, which is 36 m.

AI explanation

Because the sphere is drawn into a wire, the volume of the sphere equals the volume of the cylindrical wire, given by the formula 4/3 times pi times R cubed equals pi times r squared times height. Substituting the radius of the sphere as 3 cm and the radius of the wire as 0.1 cm, we get 4/3 times pi times 3 cubed equals pi times 0.1 squared times height. Canceling pi from both sides and solving for height gives 36 divided by 0.01, resulting in a length of 36 units.

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