Multiple choice

If a solid sphere of $3\ cm$ radius is melted and re-casted into a right circular cone whose base radius is same as that of the sphere, the height of the cone will be:

  1. $8\ cm$
  2. $12\ cm$
  3. $6\ cm$
  4. $5\ cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of sphere = (4/3) * pi * r^3 = (4/3) * pi * 27 = 36 * pi. Volume of cone = (1/3) * pi * r^2 * h. Since base radius r = 3, (1/3) * pi * 9 * h = 36 * pi. Thus, 3h = 36, so h = 12.

AI explanation

By equating volumes, the volume of the sphere equals the volume of the cone, using the formulas (4/3) * pi * r^3 and (1/3) * pi * r^2 * h. Substituting the radius of 3 cm gives (4/3) * pi * 3^3 = (1/3) * pi * 3^2 * h. Solving for h yields 36 / 3, which equals 12 cm.

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