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iop360 Group Title

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

  • 2 years ago
  • 2 years ago

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  1. iop360 Group Title
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    \[V =\frac{ 4 }{ 3 }\pi r^3\] \[surface area = 4\pi r^2\]

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

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

    • 2 years ago
  4. tjones89 Group Title
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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)

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

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

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

    • 2 years ago
  8. tjones89 Group Title
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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

    • 2 years ago
  9. iop360 Group Title
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    back

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

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

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

    • 2 years ago
  13. tjones89 Group Title
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    I got 3%

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

    • 2 years ago
  15. tjones89 Group Title
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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

    • 2 years ago
  16. tjones89 Group Title
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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

    • 2 years ago
  17. tjones89 Group Title
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    sorry ugly formatting

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

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

    • 2 years ago
  20. iop360 Group Title
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    thanks!

    • 2 years ago
  21. tjones89 Group Title
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    np :)

    • 2 years ago
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