Volume by integration

  • #1

Homework Statement


I have the attached problem ,and Show my answer and solution,

My answer is 3.14*(15 -8ln4)
While book answer 3.14(15+8ln)
IMG_2214.jpg

Can any one point to the mistake I made???
 

Answers and Replies

  • #2
Charles Link
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Your calculation looks correct to me. I don't see any obvious errors.
 
  • #3
Your work also looks good to me.
The one thing I noticed is the answer from the book would be right if you take the negative away from the 1.

I'm guessing the book has a typo.
 
  • #4
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While book answer 3.14(15+8ln)
If this is actually the book's answer, it makes no sense without something following ln.
 
  • #5
Thanks
Absolutely right, but draw the function, you will see that volume is almost as his answer(using geometry not integration),and that why I am confused.
 
  • #6
Ray Vickson
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Absolutely right, but draw the function, you will see that volume is almost as his answer(using geometry not integration),and that why I am confused.
If you think that the book's answer ##\pi (15+8 \ln(4))## is close to the correct answer you are very much mistaken. The correct answer is yours, except that the approximation ##\pi = 3.14## is way too crude---just leave it as symbolic ##\pi## until it comes time to evaluate the final answer numerically. Look at the following:
[tex]\begin{array}{rccc}
\pi (15 - 8 \ln\,4 )& \doteq & 12.28251236 & \doteq & 12.3 \\
\pi (15 + 8 \ln\,4 ) & \doteq & 81.96526726 & \doteq & 82.0 \\
\pi 15 & \doteq & 47.12388981 & \doteq & 47.1
\end{array}

[/tex]
 
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  • #7
you
If you think that the book's answer ##\pi (15+8 \ln(4))## is close to the correct answer you are very much mistaken. The correct answer is yours, except that the approximation ##\pi = 3.14## is way too crude---just leave it as symbolic ##\pi## until it comes time to evaluate the final answer numerically. Look at the following:
[tex]\begin{array}{rccc}
\pi (15 - 8 \ln\,4 )& \doteq & 12.28251236 & \doteq & 12.3 \\
\pi (15 + 8 \ln\,4 ) & \doteq & 81.96526726 & \doteq & 82.0 \\
\pi 15 & \doteq & 47.12388981 & \doteq & 47.1
\end{array}

[/tex]
You are right his answer is not logical,

Thanks
 

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