Multiple choice

A solid cylinder of iron, the radius of whose base is $2$ cm and height $9$ cm, is melted and turned into sphere. The radius of the sphere so formed is

  1. $6$ cm
  2. $5$ cm
  3. $4$ cm
  4. $3$ cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = pi * 2^2 * 9 = 36pi. Volume of sphere = (4/3) * pi * R^3. Setting them equal: 36pi = (4/3) * pi * R^3. 36 = (4/3) * R^3. 27 = R^3. R = 3.

AI explanation

Using the cylinder volume formula V = pi * r^2 * h, the volume of the iron cylinder is pi * 2^2 * 9 = 36 * pi. Setting this equal to the volume of the sphere, (4/3) * pi * r^3 = 36 * pi, and solving for r gives r^3 = (3/4) * 36 = 27. Taking the cube root of 27 gives a sphere radius of 3 cm. The result is 3 cm.

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