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anonymous

  • one year ago

a can of beans has surface area 359 cm^2. Its height is 10 cm. What is the radius of the circular top?

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  1. anonymous
    • one year ago
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    Do you know the formula for calculating the surface area of a sphere?

  2. anonymous
    • one year ago
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    2pir^2+2pirh?

  3. anonymous
    • one year ago
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    oh wait just pir^2?

  4. anonymous
    • one year ago
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    Pir^2 is just the surface area of one lid, so for the 2 lids it would be 2Pir^2 what is the formula for the walls?

  5. anonymous
    • one year ago
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    2pirh?

  6. anonymous
    • one year ago
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    is the answer 4.06?

  7. anonymous
    • one year ago
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    im following the steps the teacher gave me for notes but i keep getting them wrong. This is the 5th problem like this I've attempted to do.

  8. anonymous
    • one year ago
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    The wall of the can would be circumference x height. (The height is given). What is the circumference?

  9. anonymous
    • one year ago
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    I did not calculate the answer. I'm doing step by step with you.

  10. anonymous
    • one year ago
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    I apologize, you wrote the correct answer earlier. The surface area of the wall is 2 pirh.

  11. anonymous
    • one year ago
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    And what you wrote the very first time "2pir^2+2pirh" is also correct.

  12. anonymous
    • one year ago
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    359=2pir^2 + 20pir?

  13. anonymous
    • one year ago
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    So far looks good. It may be easier to factor out a 2 and write it as 359 = 2 (pir^2 + 10pir). You're on the right track.

  14. anonymous
    • one year ago
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    in my notes my teacher has me equal it out to 0 following this it would be 0 = 2pir^2+20pir-359

  15. phi
    • one year ago
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    this one is more painful than that. How about divide all term by 2pi and write it as \[ r^2 + 10 r - \frac{359}{2 \pi} = 0 \] if we use a calculator, that is about \[ r^2 + 10 r - 57.1366=0 \] to find r we could use the quadratic formula

  16. anonymous
    • one year ago
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    after that step i'm getting very confused

  17. anonymous
    • one year ago
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    Give me a few minutes. I'll try it the way you have it in your notes.

  18. anonymous
    • one year ago
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    x=-b+- sqr rt, b^2-4ac / 2a

  19. anonymous
    • one year ago
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    quadratic formula?

  20. anonymous
    • one year ago
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    okay thank you

  21. phi
    • one year ago
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    yes, quadratic formula. if you first divide by 2pi most of the numbers get a bit smaller and you would have a=1, b=10 , c= 57.1366

  22. anonymous
    • one year ago
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    -10pi+- sq rt. 100-4(!)(57.1366)/2?

  23. phi
    • one year ago
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    if you are doing \[r^2 + 10 r - 57.1366=0 \] -b is -10 (not -10pi) a=1 so 4ac is just 4*-57.1366 (notice c is negative)

  24. phi
    • one year ago
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    so \[ \frac{-10+ \sqrt{100 + 228.5465}}{2} \]

  25. phi
    • one year ago
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    I would pick the + sqrt because otherwise we get a negative radius

  26. anonymous
    • one year ago
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    114.27325

  27. anonymous
    • one year ago
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    am i calculating this right

  28. anonymous
    • one year ago
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    i feel so wrong

  29. phi
    • one year ago
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    yes, not correct.

  30. anonymous
    • one year ago
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    what am i doing wronnggggg

  31. phi
    • one year ago
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    can you get this far: \[ \frac{-10+ \sqrt{100 + 228.5465}}{2}\] (by the way for c = -359/(2pi) I would use all the digits the calculator has)

  32. anonymous
    • one year ago
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    -28.56831228

  33. phi
    • one year ago
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    for \[ r^2 + 10 r - 57.1366=0 \] a=1, b=10, c= -57.1366 (roughly) let's first figure out b^2 -4 * a *c that is 100 - 4 * 1 * -57.1366 what does that simplify to ?

  34. anonymous
    • one year ago
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    i'm getting -118.5465.

  35. phi
    • one year ago
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    4*-57.1366= -228.5465 now do 100 - (-228.5465)

  36. anonymous
    • one year ago
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    I made a mistake in my calculation. I don't want to post until I figure out where the error is.

  37. phi
    • one year ago
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    notice it is minus a minus. that makes it a +

  38. anonymous
    • one year ago
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    OHHHHHHH, 328.5465

  39. anonymous
    • one year ago
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    i forgot the other minus

  40. phi
    • one year ago
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    yes. so make a note: Be careful about the minus signs (they are evil) now find the square root.

  41. anonymous
    • one year ago
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    4.062925852??????

  42. phi
    • one year ago
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    yes, that looks good. do they want the answer rounded ?

  43. anonymous
    • one year ago
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    yes, 4.06

  44. anonymous
    • one year ago
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    so i was right earlier. Thank you both so much for your help!

  45. anonymous
    • one year ago
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    Sorry I wasn't able to help you through it

  46. phi
    • one year ago
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    if we use 4.06 in the original formula we get 358.67 or about 359, so it checks out.

  47. anonymous
    • one year ago
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    If it helps I'll post how to do it in a calculator that has fractions

  48. anonymous
    • one year ago
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    \[\frac{ -20 + \sqrt{20^2+ 8(\frac{ 359 }{ \pi })} }{ 4 }\]

  49. anonymous
    • one year ago
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    If your calculator allows you to enter the above equation (in one step) you'll get the same answer. I put in + 8 since the two negatives become positive.

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