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anonymous

  • one year ago

Challenge: The distance around the middle of a sphere (the circumference) equals 37.699 in. What is the surface area of the sphere?

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  1. anonymous
    • one year ago
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    I got 4,464.88 in^2.

  2. anonymous
    • one year ago
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    Is it correct?

  3. anonymous
    • one year ago
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    @dan815 @pooja195 @ganeshie8

  4. anonymous
    • one year ago
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    @Hero

  5. jdoe0001
    • one year ago
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    yeap \(\bf \textit{surface of a sphere}=4\pi r^2\qquad r=\cfrac{37.699}{2}\qquad 4\cdot \pi \cdot \left( \cfrac{37.699}{2} \right)^2 \approx 4464.88\)

  6. jdoe0001
    • one year ago
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    \(\bf \textit{surface of a sphere}=4\pi r^2\qquad r=\cfrac{37.699}{2}\qquad \\ \quad \\ 4\cdot \pi \cdot \left( \cfrac{37.699}{2} \right)^2 \approx 4464.88\)

  7. anonymous
    • one year ago
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    Thanks!!

  8. anonymous
    • one year ago
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    @jdoe0001

  9. anonymous
    • one year ago
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    What we did earlier was wrong

  10. anonymous
    • one year ago
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    C = 2πr 37.699 = 2πr 37.699 / 2π = r 59.22 ≈ r The radius is approximately 59.22 inches. SA = 4π59.22^2 SA ≈ 44070.37 The surface area is approximately 44,070.37 in^2.

  11. anonymous
    • one year ago
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    That's my work for my revision

  12. Loser66
    • one year ago
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    First off, you need find r Yes

  13. Loser66
    • one year ago
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    correct

  14. anonymous
    • one year ago
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    @Loser66

  15. anonymous
    • one year ago
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    what is correct?? XD

  16. Loser66
    • one year ago
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    The last one.

  17. anonymous
    • one year ago
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    heey, @jdoe0001 , what we did earlier was wrong, we thought the circumference was the diameter and worked from there

  18. Loser66
    • one year ago
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    while I tried to guide you, you posted the correct one, so that I just say yes.

  19. anonymous
    • one year ago
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    Ok, thanks!

  20. jdoe0001
    • one year ago
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    hmmm the distance around the middle of a sphere, sounds to me like the diameter :)

  21. Loser66
    • one year ago
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    @jdoe0001 Hey, invisible friend, no more invisible??? hahaha

  22. anonymous
    • one year ago
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    But in the question it says it's the circumference

  23. jdoe0001
    • one year ago
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    hehe

  24. anonymous
    • one year ago
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    It's the distance AROUND, not the distance from one end to another

  25. jdoe0001
    • one year ago
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    lemme be back in a bit

  26. anonymous
    • one year ago
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    ok

  27. anonymous
    • one year ago
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    u got it??

  28. anonymous
    • one year ago
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    @jdoe0001

  29. jdoe0001
    • one year ago
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    @sewandowski ... hold the mayo

  30. jdoe0001
    • one year ago
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    so the circumference is 37.699 we also know that the circumference of any circle is \(2\pi r\) thus we could say that \(\bf circumference = 37.699\qquad circumference=2\pi r\qquad thus \\ \quad \\ 37.699=2\pi r\implies {\color{brown}{ \cfrac{37.699}{2\pi } }}=r \\ \quad \\ \quad \\ \textit{surface area}=4\pi {\color{brown}{ r}}^2\to 4\pi \cdot \left( {\color{brown}{ \cfrac{37.699}{2\pi } }} \right)^2\to 4\pi \cfrac{37.699^2}{2^2\pi^2}\to \cancel{4\pi} \cfrac{37.699^2}{\cancel{4\pi}\pi }\)

  31. anonymous
    • one year ago
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    Heey, just finished the test, it was another answer :/

  32. anonymous
    • one year ago
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    Nevermind, thanks for the help but I need help in another problem, so I'll close this one and make another one. Thanks anyways!

  33. jdoe0001
    • one year ago
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    k

  34. mathstudent55
    • one year ago
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    \(r = \dfrac{37.699 ~in.}{2 \pi} = 5.99998 ~in.\) \(A = 4 \pi r^2 = 4 \times \pi \times (5.99998~in.)^2 = 452.39~in.^2\)

  35. mathstudent55
    • one year ago
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    @sewandowski Before you go look at this. You wrote above: C = 2πr 37.699 = 2πr 37.699 / 2π = r 59.22 ≈ r When you solve a problem, you need to do the operations, but you also need to confirm that answers make sense. If the circumference of a circle is approx. 38 in., how can the radius of the circle be 59.22 in.? It's impossible for the radius of a circle to be larger than the circumference.

  36. mathstudent55
    • one year ago
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    Your mistake above is this: How do you calculate \(\dfrac{37.699}{2 \pi} \) ? You can use your calculator and calculat4e first 2 * pi = 6.28 Then do 37.699/6.28 Or you can do 37.699 / 2 / pi You need to divide 37.699 by 2 and divide the result by pi, not multiply by pi like you did.

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