Find the Mistake in Calculating Volume by Integration

[keewansadeq]

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)

Can anyone point to the mistake I made?

 

[Charles Link]

Your calculation looks correct to me. I don't see any obvious errors.

 

[Ethan Godden]

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.

 

[Mark44]

While book answer 3.14(15+8ln)

If this is actually the book's answer, it makes no sense without something following ln.

 

[keewansadeq]

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.

 

[Ray Vickson]

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.

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:
$$\begin{array}{rccc} \pi (15 - 8 \ln\,4 )& \doteq & 12.28251236 & \doteq & 12.3 \\ \pi (15 + 8 \ln\,4 ) & \doteq & 81.96526726 & \doteq & 82.0 \\ \pi 15 & \doteq & 47.12388981 & \doteq & 47.1 \end{array}$$

 

[keewansadeq]

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:
$$\begin{array}{rccc} \pi (15 - 8 \ln\,4 )& \doteq & 12.28251236 & \doteq & 12.3 \\ \pi (15 + 8 \ln\,4 ) & \doteq & 81.96526726 & \doteq & 82.0 \\ \pi 15 & \doteq & 47.12388981 & \doteq & 47.1 \end{array}$$

You are right his answer is not logical,

Thanks