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anonymous

  • 5 years ago

A figure shows a cubical box with a sphere that just fits inside.That is,the length,width,and height of the box are each equal to the diameter of the ball.What percent to the nearest tenth of the volume of the box is not occupied by the ball?

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  1. amistre64
    • 5 years ago
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    lol again?

  2. amistre64
    • 5 years ago
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    x^3 - still dont know the formula for a Sphere volume = free volume

  3. amistre64
    • 5 years ago
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    4pir^3 ------ ?? sounds familiar 3

  4. anonymous
    • 5 years ago
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    I have 4/3 pi r^3 as the sphere volume

  5. anonymous
    • 5 years ago
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    I don't understand sphere volume = free volume

  6. amistre64
    • 5 years ago
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    r = x so lets run with that. it means that the sphere eats up so much of the boxes volume that whatever is not taken up by the sphere is "free"....empty space

  7. amistre64
    • 5 years ago
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    x^3 - 4pi(x^3) ------- 3 3x^3 - 4pi(x^3) -------------- 3 x^3(3 - 4pi) ---------- should be the free space in the box. 3

  8. anonymous
    • 5 years ago
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    What is the box volume to minus the sphere volume?

  9. amistre64
    • 5 years ago
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    suppose you have a bathtub filled with bubble bath till lits almost overflowing.... when you get in, the volume of water that flows out is taken up by the volume of your body getting in; when you get out of the tub, the amount of water left in is the stuff that didnt overflow to begin with and it is equal to: volume of tub - volume of you...

  10. anonymous
    • 5 years ago
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    o.k. I can imagine that,but in order for me to resolve this problem I need the formula of the volume for the box and sphere.

  11. amistre64
    • 5 years ago
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    that is correct: the volume of a square cubical box is: side times side times side...or side^3; lets call it x^3 :)

  12. amistre64
    • 5 years ago
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    the radius of the sphere is x/2 so my initial figureing was misappropriated.....

  13. anonymous
    • 5 years ago
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    am I suppose to subtract something?

  14. anonymous
    • 5 years ago
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    how do I input the information into my calculator?

  15. anonymous
    • 5 years ago
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    What is the percent?

  16. amistre64
    • 5 years ago
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    do you have a "real" value for the sides of the box? or the radius of the sphere? without that, you are left with a formula with variables in it

  17. amistre64
    • 5 years ago
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    if we assume the box side is twice the radius of the sphere; we get: 4pi(x^3) 8x^3 - ------- for the free volume in the box 3

  18. anonymous
    • 5 years ago
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    The problem is how it's stated -no numbers.

  19. anonymous
    • 5 years ago
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    the length,width,and height of the box are equal to the diameter of the ball

  20. amistre64
    • 5 years ago
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    24x^3 - 4pi(x^3) ---------------- x100 = percent free 24x^3

  21. anonymous
    • 5 years ago
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    I don't understand how you got your numbers

  22. amistre64
    • 5 years ago
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    the volume of a box is (8x^3) 2x * 2x * 2x = 8x^3

  23. anonymous
    • 5 years ago
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    I need the percent to the nearest tenth of a volume of the box not occupied by the ball

  24. amistre64
    • 5 years ago
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    do you agree that the volume of the box is 8x^3? if there is a figure that goes with the question....tell me, does it show a number for the raduis of the sphere or perhaps a number for the side of the box?

  25. anonymous
    • 5 years ago
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    Nope,the illustration only displays a ball inside of a cubicle box

  26. amistre64
    • 5 years ago
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    then we will have to see if our variables cancel out at some point in the process........ when we get to the end of the process, lets see if we get a "percentage" that doesnt include a variable then.... you agree?

  27. anonymous
    • 5 years ago
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    Yes,agree.

  28. amistre64
    • 5 years ago
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    I beleive I was up to here in the process then :) 24x^3 - 4pi(x^3) ---------------- x100 = percent free 24x^3

  29. anonymous
    • 5 years ago
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    I'm just having a difficult time with the process.

  30. amistre64
    • 5 years ago
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    I know.... but what we are doing is just substituting letter for number and working it thru.....

  31. amistre64
    • 5 years ago
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    lets say the radius of the sphere is equal to "x" the radius of the sphere is exactly "half" the measurement of a side of the box; so 2x = the width, the height and the depth of the box. w*h*d = 2x * 2x * 2x = 8x^3 you agree?

  32. anonymous
    • 5 years ago
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    So,if I were to input your equation into my calculator I got the answer: 13823.9091

  33. amistre64
    • 5 years ago
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    i havent checked my own propensity for error yet :) lets get to the end of the process first ok?

  34. amistre64
    • 5 years ago
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    volume of box = 8x^3 volume of sphere = 4pi(x^3) -------- right? 3

  35. anonymous
    • 5 years ago
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    o.k. then what?

  36. amistre64
    • 5 years ago
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    (3)8x^3 4pi(x^3) 24(x^3) - 4pi(x^3) ------- - ------- = ---------------- 3 3 3

  37. amistre64
    • 5 years ago
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    which equals: 4x^3(6 - pi) ---------- 3 we divide this "value" by the volume of the box: 8x^3 4x^3(6 - pi) ---------- / 8x^3 3 4x^3(6 - pi) ---------- we can cancel out like terms and reduce this. 24x^3

  38. anonymous
    • 5 years ago
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    is this the simplest,straightforward method?

  39. amistre64
    • 5 years ago
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    (6-pi) ----- = 1 - pi/6 this is a decimal value 6 we multiply it by 100 to get a number for the % 100(1-pi/6) = 100 - 50pi/3. the calculator says .........its the simplest and straight forward answer yes; do you really think Id waste my time helping you for a joke?.....dont interupt :)

  40. anonymous
    • 5 years ago
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    :) sorry.

  41. amistre64
    • 5 years ago
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    47.64 % is the result I get :)

  42. anonymous
    • 5 years ago
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    Wow! So why do we have the equations over 3?

  43. amistre64
    • 5 years ago
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    becasue 100pi/6 reduces to 50pi/3

  44. amistre64
    • 5 years ago
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    we could stop at: 100(1-(pi/6)) and get the same results i spose :)

  45. anonymous
    • 5 years ago
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    Hmm...I really need to look over the whole thing and digest this.

  46. amistre64
    • 5 years ago
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    you do that..... and since the "x" variable vanishes in the end, we probably could have went with a value of x=1 to begin with; but i wasnt sure if it was going to work out that well :)

  47. anonymous
    • 5 years ago
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    O.k. well,thank you for your trouble and time.

  48. amistre64
    • 5 years ago
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    youre welcome :)

  49. anonymous
    • 5 years ago
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    oh.... amistre :)

  50. amistre64
    • 5 years ago
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    ....yes???

  51. anonymous
    • 5 years ago
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    help please <3

  52. amistre64
    • 5 years ago
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    ....post a new question so I aint gotta scroll :)

  53. anonymous
    • 5 years ago
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    ok

  54. anonymous
    • 5 years ago
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    Write the trigonometric expression in terms of sine and cosine, and then simplify. sec(x)/csc(x)

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