Multiple choice

A solid sphere with a radius of 9 cm is melted and recast into cylindrical rods, each with a radius of 1.5 cm and a length of 24 cm. How many rods are produced?

  1. 18

  2. 21

  3. 12

  4. 15
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A Correct answer
Explanation

Volume of sphere = (4/3) * pi * 9^3 = 972 * pi. Volume of one rod = pi * 1.5^2 * 24 = pi * 2.25 * 24 = 54 * pi. Number of rods = 972 / 54 = 18.

AI explanation

The volume of the melted sphere is conserved, calculated using the formula 4 divided by 3 times pi times r cubed, giving 4 divided by 3 times pi times 9 cubed, which equals 972 times pi. The volume of one cylindrical rod is found using pi times r squared times height, resulting in pi times 1.5 squared times 24, which equals 54 times pi. Dividing the total volume of the sphere by the volume of a single rod gives 972 times pi divided by 54 times pi. This calculation shows that 18 rods can be produced.

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