Multiple choice

A solid metallic spherical ball of diameter $6$cm is melted and recast into a cone with diameter of the base as $12$cm. The height of the cone is _________.

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

The volume of the sphere is (4/3)*pi*r^3 = (4/3)*pi*3^3 = 36*pi. The volume of the cone is (1/3)*pi*R^2*h = (1/3)*pi*6^2*h = 12*pi*h. Setting volumes equal: 36*pi = 12*pi*h, so h = 3.

AI explanation

Using the conservation of volume, the volume of the spherical ball equals the volume of the cone. The radius of the sphere is 3 cm and the radius of the cone base is 6 cm. Applying the formulas, (4/3) * pi * (3)^3 = (1/3) * pi * (6)^2 * h, which simplifies to 36 * pi = 12 * pi * h; solving for h gives 3 cm.

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