Multiple choice

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is

  1. 4 cm

  2. 3 cm

  3. 2 cm

  4. 6 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = pi * 1^2 * 16 = 16 * pi. Volume of 12 spheres = 12 * (4/3) * pi * r_s^3 = 16 * pi * r_s^3. Equating: 16 * pi = 16 * pi * r_s^3, so r_s^3 = 1, r_s = 1. Diameter = 2 * r_s = 2 cm.

AI explanation

The volume of the cylinder equals the combined volume of the 12 spheres. The cylinder has a radius of 1 cm and a height of 16 cm, so its volume is 16 pi cubic cm. Setting 12 times 4/3 times pi times r cubed equal to 16 pi gives r cubed equals 1. The radius of each sphere is 1 cm, making the diameter 2 cm.

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