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anonymous

  • one year ago

The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r?

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  1. mathstudent55
    • one year ago
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    Do you know the formula of the volume of a cone?

  2. anonymous
    • one year ago
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    what are the choices?

  3. anonymous
    • one year ago
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    v = π r 2 h 3

  4. mathstudent55
    • one year ago
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    is there a fraction there? Is there an exponent there?

  5. anonymous
    • one year ago
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    A. V= 2/3 PIE R2 B. V= 4/3 PIE R3 C. V= 1/3 PIE R3 D. V= 1/3 PIE R2

  6. mathstudent55
    • one year ago
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    Do you mean this for the formula? \(\LARGE V_{cone} = \dfrac{\pi r^2 h}{3}\)

  7. anonymous
    • one year ago
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    YEAH

  8. mathstudent55
    • one year ago
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    Great. That is the correct formula. Notice the formula uses r to mean radius of the base, and h to mean the height of the cone.

  9. mathstudent55
    • one year ago
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    Now let's look at your problem's cone. The radius is r. What is the diameter, d, compared to the radius?

  10. mathstudent55
    • one year ago
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    In any circle, what is the relationship between the diameter and the radius?

  11. mathstudent55
    • one year ago
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    |dw:1435165536451:dw|

  12. mathstudent55
    • one year ago
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    What is the diameter in terms of the radius?

  13. anonymous
    • one year ago
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    D=2r

  14. mathstudent55
    • one year ago
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    @jazmine24 Do you understand that? d = 2r The diameter is twice the radius.

  15. anonymous
    • one year ago
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    yes i do understand

  16. mathstudent55
    • one year ago
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    Great. Now we need to find the height. We are told the height is twice the diameter. h = 2d, but we know d = 2r, so we have: h = 2(2r) h = 4r Now we have the radius is r, and the height is 4r. Now we can use the formula: \(\Large V_{cone} = \dfrac{\pi r^2 h}{3} \) \(\Large V_{cone} = \dfrac{\pi r^2 (4r)}{3} \) \(\Large V_{cone} = \dfrac{4 \pi r^3}{3} \)

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