[Blindmath] volume of rotational solids (calculus)

[Steve Jacobson]

To add encouragement, when I took calculus many years ago, my professor actually concluded that I seemed to have a better grasp of the revolution of 
solids because I tended to picture it in my mind in three dimensions rather than trying to represent it on a two dimensional surface.  I am lucky to be able to 
picture relationships pretty well, but I think it is worth trying to at least understand what is happening graphically and going from there.  As was mentioned, it 
wasn't that essential that I be able to do a three dimensional graph, although I think the professor did ask me to describe what I was picturing.  Admittedly, 
this does stretch the imagination, though.

Best regards,

Steve Jacobson

On Tue, 8 Mar 2011 21:59:17 +0000, Salisbury, Justin Mark wrote:

>Hi Alex,

>    Are you taking Calculus II?  If so, I'm pretty sure that they aren't expecting you to integrate any functions that are undefined.  I'm pretty sure you'll be 
integrating continuous functions.  If you're asking how to know which bound lies inside the other one, that's generally a matter of a distance from the axis of 
rotation.  I hope that you can mentally conceptualize which functions lie inside other ones.  Otherwise, you'll have to use a distance formula to the axis of 
rotation for points on each equation.  If you just have the understanding that you're calculating the distance between two or more equations and then 
rotating it to turn area into volume, you should have a thorough enough understanding of what you're doing.  If you want to contact me off-list for humorous 
real-life examples, feel free.  Sighted mathematicians really only use sketches to help themselves understand what they're doing.  Many advanced 
mathematicians never even draw the functions before beginning their computations.  I think you'll be just fine as long as you know that you're accomplishing 
and know which functions lie inside the others.

>Good luck!

>Justin

>Justin M. Salisbury
>Undergraduate Student
>The University Honors Program
>East Carolina University
>salisburyj08 at students.ecu.edu

>"It is the mark of an educated mind to be able to entertain a thought without accepting it."    -Aristotle
>________________________________________
>From: blindmath-bounces at nfbnet.org [blindmath-bounces at nfbnet.org] on behalf of Alex Hall [mehgcap at gmail.com]
>Sent: Tuesday, March 08, 2011 4:30 PM
>To: Blind Math list for those interested in mathematics
>Subject: [Blindmath] volume of rotational solids (calculus)

>Hi all,
>This is not a request for help in finding this sort of thing. Rather,
>I am wondering if it can be done purely algebraically so I do not have
>to try to imagine the graph. Example:

>Find the volume of the solid formed by rotating the function y=x^2
>around the x-axis from x=0 to x=4.

>This one is a pretty simple example, and should be pi*x^5/5, I think.
>This is using the Disk Method, but what happens with the Washer method
>or the Shell method, where you might have space in the solid where the
>function is not defined? Currently, I have to try to imagine the graph
>to "see" the radius to use, any undefined portions, and so on. What I
>am wondering is if anyone has dealt with this and has found any way to
>do it all with algebra or some other non-graphical method. If so,
>please share! Thanks.

>--
>Have a great day,
>Alex (msg sent from GMail website)
>mehgcap at gmail.com; http://www.facebook.com/mehgcap

>_______________________________________________
>Blindmath mailing list
>Blindmath at nfbnet.org
>http://www.nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>To unsubscribe, change your list options or get your account info for Blindmath:
>http://www.nfbnet.org/mailman/options/blindmath_nfbnet.org/salisburyj08%40students.ecu.edu

>_______________________________________________
>Blindmath mailing list
>Blindmath at nfbnet.org
>http://www.nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>To unsubscribe, change your list options or get your account info for Blindmath:
>http://www.nfbnet.org/mailman/options/blindmath_nfbnet.org/steve.jacobson%40visi.com