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three cones have a volume of 192π cm³.Cone A has a radius of 2 cm. Cone B has a radius of 3 cm. Cone C has a radius of 4 cm. find the height of each one

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sqdancefan

9514 1404 393

Answer:

  A: 144 cm

  B: 64 cm

  C: 36 cm

Step-by-step explanation:

The volume of a cone is given by ...

  V = (1/3)πr²h

Solving for h, we get ...

  3V/(πr²) = h

Filling in the given values, we get ...

  3(192π)/(πr²) = h

  576/r² = h

Then the heights of the different cones are ...

  A: r = 2, h = 576/4 = 144 . . . cm

  B: r = 3, h = 576/9 = 64 . . . cm

  C: r = 4, h = 576/16 = 36 . . . cm

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