Multiple choice

The base radius and height of a right circular solid cone are $12 cm$ and $24 cm$, respectively. It is melted and recast into spheres of diameter $6 cm$ each. Find the number of spheres so formed.

  1. $48$
  2. $40$
  3. $32$
  4. $24$
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C Correct answer
Explanation

Volume of cone = (1/3) * pi * r^2 * h = (1/3) * pi * 12^2 * 24 = 1152 * pi. Volume of sphere = (4/3) * pi * r^3 = (4/3) * pi * 3^3 = 36 * pi. Number of spheres = 1152 * pi / 36 * pi = 32.

AI explanation

Equate the volume of the solid cone to the total volume of the newly formed spheres to find the number of spheres. The volume of the cone is calculated as one third times pi times twelve squared times twenty-four, which equals 1152 pi. The radius of each newly formed sphere is three cm, making the volume of one sphere four thirds times pi times three cubed, which equals 36 pi. Dividing the total volume of 1152 pi by the individual sphere volume of 36 pi results in 32 spheres.

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