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marigirl

  • one year ago

can you please check over why my method is incorrect for this question. Topic differentiation A Cylinder of height h and radius r is inside a sphere of of radius 10. find the value of r that will maximise volume of cylinder

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  1. marigirl
    • one year ago
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    Volume of a cylinder is v=pi r^2*h so i went about getting an expression or h to substitute in by using similar triangles

  2. marigirl
    • one year ago
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  3. marigirl
    • one year ago
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    so i used similar triangles and obtained h=20-2r .. the model answers showed that they used pythagoras.. why is my methods incorrect?

  4. amistre64
    • one year ago
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    height is based off a curve, not a line

  5. amistre64
    • one year ago
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    height = sqrt(10^2 - x^2)

  6. amistre64
    • one year ago
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    oh, and even tho thats pythagorean, its really based off of the equation for the circle of the sphere

  7. marigirl
    • one year ago
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    but if u take the into consideration the height and radius measurements from the origin of x and y axis - wont it be a straight line?

  8. amistre64
    • one year ago
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    |dw:1444434018307:dw|

  9. amistre64
    • one year ago
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    all points equidistant from the center ... in this case the origin ... is the equation x^2 + y^2 = r^2

  10. amistre64
    • one year ago
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    height is measured as 2y in this case. radius is x

  11. marigirl
    • one year ago
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    but if u take the into consideration the height and radius measurements from the origin of x and y axis - wont it be a straight line?

  12. amistre64
    • one year ago
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    repeating faulty arguments do not make them any more correct ...

  13. Loser66
    • one year ago
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    |dw:1444437755660:dw|

  14. Loser66
    • one year ago
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    where r is the radius of the cylinder, h is the height of it

  15. marigirl
    • one year ago
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    i am not trying sound smart .. i was just generally thinking about these problems... i did a problem before with a cylinder inside a triangle..

  16. amistre64
    • one year ago
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    a sphere is not a triangle :)

  17. amistre64
    • one year ago
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    a cone would have a linear setup ... since its profile is a triangle

  18. marigirl
    • one year ago
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    in that case- similar triangle works.. but u cant apply the height is based off a curve...I am sorry i didnt mean to sound arrogant.. im just thinking

  19. amistre64
    • one year ago
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    thinking is good ... just some thoughts are worse than others

  20. marigirl
    • one year ago
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    I appreciate your answer. thank you

  21. amistre64
    • one year ago
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    x^2 + y^2 = 10^2 is the equation of your circle, which your cylindar sets in y = sqrt(100-x^2) is the top of the sphere, which is 1/2 the height of the cylindar from the x axis

  22. marigirl
    • one year ago
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    yes i get how that formula is used here. so i guess it really comes down to what the cylinder is inscribed inside...if it is a sphere then its properties would be different to a cone. Thank you

  23. amistre64
    • one year ago
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    V = pi r^2 h, r=x, and h=2sqrt(100-x^2) V' = pi (2r r' + r^2 h') V' = 0 when, 2r r' + r^2 h' = 0 just some of my thoughts is all

  24. amistre64
    • one year ago
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    correct, good luck :)

  25. marigirl
    • one year ago
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    thank you!

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