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anonymous

  • one year ago

A plane intersects a sphere to form a circle as shown in the figure. The distance from the center of the circle to the center of the sphere is 10in. If the area of the circle formed by the intersection is 576 pi inches squared, what is the volume of the​ sphere?

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  1. anonymous
    • one year ago
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    |dw:1443066944419:dw|

  2. anonymous
    • one year ago
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    @ganeshie8 @mathstudent55 @Zale101 @kohai @dan815 @zepdrix

  3. anonymous
    • one year ago
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    I'm totally lost on this one, I keep getting similar problems wrong, the last equaled out to 4000/3 pi in.^3

  4. ganeshie8
    • one year ago
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    Hey if psble could you attach the original diagram

  5. ganeshie8
    • one year ago
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    I'm finding it a bit hard to relate the word problem to the picture that you have drawn

  6. anonymous
    • one year ago
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    the picture i drew is pretty much it.

  7. anonymous
    • one year ago
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    |dw:1443067700784:dw|

  8. ganeshie8
    • one year ago
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    Ok got you

  9. anonymous
    • one year ago
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    It wants me to find the volume, I even tried the V=4/3*3.14*r^3

  10. ganeshie8
    • one year ago
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    Think of the given diagram as a small spherical fish tank, 10cm represents the center of top surface to the center of fish tank : |dw:1443067804228:dw|

  11. ganeshie8
    • one year ago
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    They gave you surface area of the top surface : \(576\pi\) Say, the radius of top surface is \(r\) : |dw:1443067992574:dw|

  12. anonymous
    • one year ago
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    r=10 ?

  13. ganeshie8
    • one year ago
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    \[\pi r^2 = 576\pi\] solve \(r\)

  14. anonymous
    • one year ago
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    r=24 ?

  15. ganeshie8
    • one year ago
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    Yes, the radius of top circular disk surface is \(24\) : |dw:1443068220493:dw|

  16. ganeshie8
    • one year ago
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    Next, see if you can find the radius of sphere : |dw:1443068276532:dw|

  17. anonymous
    • one year ago
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    would I substitute 24 as r into the same equation?

  18. ganeshie8
    • one year ago
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    do you see a right triangle with sides \(10, 24, R\) ? you need to setup an equation and find the value of \(R\)

  19. anonymous
    • one year ago
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    which equation would I use? A=1/2 bh? sorry....

  20. ganeshie8
    • one year ago
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    when you see a right triangle, you should think of "pythagoras theorem"

  21. anonymous
    • one year ago
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    10^2+24^2=676

  22. ganeshie8
    • one year ago
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    yes take square root

  23. anonymous
    • one year ago
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    \[\sqrt{676} =26\]

  24. anonymous
    • one year ago
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    @ganeshie8 What do I do next?

  25. ganeshie8
    • one year ago
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    so \(26\) is the radius of sphere

  26. ganeshie8
    • one year ago
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    use volume formula of sphere and finish it off

  27. anonymous
    • one year ago
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    V=4/3*3.14*26^3 ?

  28. anonymous
    • one year ago
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    I get a huge number 73584.85

  29. ganeshie8
    • one year ago
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    Looks good!

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