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kellychick

  • 3 years ago

A crystal ball with a diameter of 2r inches is being packaged for shipment. If the crystal ball is placed inside a circular cylinder with radius r inches and height h inches, how much volume will need to be filled with padding? Assume r = 6, h = 12. (The volume of a sphere with radius r is 4πr3/3, and the volume of a right circular cylinder with radius r and height h is πr 2h.)

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  1. tcarroll010
    • 3 years ago
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    Volume of cylinder - volume of sphere. Just substitute for r and h as is given in the problem.

  2. crystal1
    • 3 years ago
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    hey thats my name

  3. kellychick
    • 3 years ago
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    So then it would be 3.14*6^2*12?

  4. tcarroll010
    • 3 years ago
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    Start with the volume of the cylinder, whose formula is given to you in the problem, (π)(r)(2)(h). Can you make the substitutions for r and h that are given in the problem? Just saw your answer. That formula for the volume of a cylinder contains a factor of 2 x r, not r^2.

  5. kellychick
    • 3 years ago
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    okay so, (3.14)(6)(2)(12) should give you the answer correct?

  6. tcarroll010
    • 3 years ago
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    That's the volume of the cylinder, which is the first part. Read my first post for your next step.

  7. kellychick
    • 3 years ago
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    okay so i take that answer, and then subtract it from the volume of a sphere?

  8. tcarroll010
    • 3 years ago
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    The volume of a sphere is not 4πr3/3 as you have it in your problem statement. It's (4πr^3)/3. You're having a small problem with writing out the formula. Use either "^" for the exponent or the equation tool. And careful about which way you perform subtraction. That particular mathematical operation is not commutative, that is, a-b does not equal b-a.

  9. kellychick
    • 3 years ago
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    okay, well the volume of the sphere is 288. and the volume of a cylinder is 144..

  10. tcarroll010
    • 3 years ago
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    Better check your math on both of those volumes. I suggest writing out your work here (type it out) so I can see where you went wrong. Start with the volume of the cylinder.

  11. kellychick
    • 3 years ago
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    (pi)(6)(2)(12)=144

  12. kellychick
    • 3 years ago
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    or is it (pi)(6)^2(12) which would equal 432

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