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iop360

  • 2 years ago

approximately by what percentage does the volume of a sphere increase if it's surface area is increased 2%?

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  1. iop360
    • 2 years ago
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    \[V =\frac{ 4 }{ 3 }\pi r^3\] \[surface area = 4\pi r^2\]

  2. iop360
    • 2 years ago
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    answer is a 3% increase ( need to know how though)

  3. iop360
    • 2 years ago
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    \[+0.02 = 8 \pi r \frac{ dr }{ dt }\] after plugging in and taking derivative of the surface area forumla:

  4. tjones89
    • 2 years ago
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    find out what percentage r changes if you increase the area by 2% and then find out what percentage volume changes when you change r by (whatever you find from the first part)

  5. tjones89
    • 2 years ago
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    i dont think you need calculus to solve this

  6. iop360
    • 2 years ago
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    how do i find the % by which r changes

  7. iop360
    • 2 years ago
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    brb, im gonna leave this question open

  8. tjones89
    • 2 years ago
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    first choose a number for r, find the surface area with this r, then change the surface area to 102% of that area and solve for r, the percent difference will be [(r2/r1)-1]*100

  9. iop360
    • 2 years ago
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    back

  10. iop360
    • 2 years ago
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    ive got a couple of ideas, ill try yours and mine

  11. iop360
    • 2 years ago
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    i chose r =1... i only got 1% for the answer hmmm

  12. iop360
    • 2 years ago
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    i think calculus is necessary

  13. tjones89
    • 2 years ago
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    I got 3%

  14. iop360
    • 2 years ago
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    what did you choose for radius

  15. tjones89
    • 2 years ago
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    r1 = 1 A1 = 4pi A2 = 4pi*1.02 r2 = sqrt(1.02) percent difference between r1 and r2 = ((sqrt(1.02)/1)-1)*100

  16. tjones89
    • 2 years ago
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    which is about 1 percent, but that's what percent the radius changes, so now we know that if the area changes 2 percent, the radius changes 1 percent, so if we find out how much the volume changes when we change the radius by 1 percent, we will have found out how much the volume changes when we change the area by 2 percent

  17. tjones89
    • 2 years ago
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    sorry ugly formatting

  18. tjones89
    • 2 years ago
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    now we find the volume using r1 and then using r2 and find the percent difference.

  19. iop360
    • 2 years ago
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    o, now i get the answer

  20. iop360
    • 2 years ago
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    thanks!

  21. tjones89
    • 2 years ago
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    np :)

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