Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

iop360

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

  • one year ago
  • one year ago

  • This Question is Closed
  1. iop360
    Best Response
    You've already chosen the best response.
    Medals 0

    \[V =\frac{ 4 }{ 3 }\pi r^3\] \[surface area = 4\pi r^2\]

    • one year ago
  2. iop360
    Best Response
    You've already chosen the best response.
    Medals 0

    answer is a 3% increase ( need to know how though)

    • one year ago
  3. iop360
    Best Response
    You've already chosen the best response.
    Medals 0

    \[+0.02 = 8 \pi r \frac{ dr }{ dt }\] after plugging in and taking derivative of the surface area forumla:

    • one year ago
  4. tjones89
    Best Response
    You've already chosen the best response.
    Medals 1

    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)

    • one year ago
  5. tjones89
    Best Response
    You've already chosen the best response.
    Medals 1

    i dont think you need calculus to solve this

    • one year ago
  6. iop360
    Best Response
    You've already chosen the best response.
    Medals 0

    how do i find the % by which r changes

    • one year ago
  7. iop360
    Best Response
    You've already chosen the best response.
    Medals 0

    brb, im gonna leave this question open

    • one year ago
  8. tjones89
    Best Response
    You've already chosen the best response.
    Medals 1

    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

    • one year ago
  9. iop360
    Best Response
    You've already chosen the best response.
    Medals 0

    back

    • one year ago
  10. iop360
    Best Response
    You've already chosen the best response.
    Medals 0

    ive got a couple of ideas, ill try yours and mine

    • one year ago
  11. iop360
    Best Response
    You've already chosen the best response.
    Medals 0

    i chose r =1... i only got 1% for the answer hmmm

    • one year ago
  12. iop360
    Best Response
    You've already chosen the best response.
    Medals 0

    i think calculus is necessary

    • one year ago
  13. tjones89
    Best Response
    You've already chosen the best response.
    Medals 1

    I got 3%

    • one year ago
  14. iop360
    Best Response
    You've already chosen the best response.
    Medals 0

    what did you choose for radius

    • one year ago
  15. tjones89
    Best Response
    You've already chosen the best response.
    Medals 1

    r1 = 1 A1 = 4pi A2 = 4pi*1.02 r2 = sqrt(1.02) percent difference between r1 and r2 = ((sqrt(1.02)/1)-1)*100

    • one year ago
  16. tjones89
    Best Response
    You've already chosen the best response.
    Medals 1

    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

    • one year ago
  17. tjones89
    Best Response
    You've already chosen the best response.
    Medals 1

    sorry ugly formatting

    • one year ago
  18. tjones89
    Best Response
    You've already chosen the best response.
    Medals 1

    now we find the volume using r1 and then using r2 and find the percent difference.

    • one year ago
  19. iop360
    Best Response
    You've already chosen the best response.
    Medals 0

    o, now i get the answer

    • one year ago
  20. iop360
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks!

    • one year ago
  21. tjones89
    Best Response
    You've already chosen the best response.
    Medals 1

    np :)

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.