Multiple choice

A solid metallic sphere with a radius of 6 cm is melted and recast into a solid cylinder. If the height of the cylinder is 8 cm, what is the radius of the cylinder's base?

  1. 2

  2. 4

  3. 5

  4. 6

  5. 8
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of sphere = (4/3) * pi * 6^3 = 288 * pi. Volume of cylinder = pi * r^2 * h = pi * r^2 * 8. Setting them equal: 288 * pi = 8 * pi * r^2. r^2 = 36, so r = 6.

AI explanation

By the volume conservation method, the volume of the solid metallic sphere equals the volume of the newly formed solid cylinder. The volume of the sphere is 4/3 times pi times 6 cubed, which equals 288 times pi cubic centimeters, and the volume of the cylinder is pi times r squared times 8. Equating the two volumes gives 288 times pi equals pi times r squared times 8; solving for r squared gives 36, meaning the base radius is 6 cm.

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