Volumes of Solids of Revolution by Shells Workings (2 Viewers)

[Axio]

Hey so I was wondering if anyone could say whether or not I can do the working out that I do for volumes questions...

Eg Q. Consider a shell of inner radius x, outer radius x + δx, and height y.

In textbooks, I see them go: δV=pi( (x+δx)^2 -x^2)y
and then by expanding and 'ignoring' the (δx)^2 term they get: 2pixyδx.

However I have always done working out like this:

r=x, h=y
SA = 2pi*r*h
SA =2pixy
therefore δV=2pixyδx as it is with respect to x.

Am I allowed to do the working out this second way (the way I always do...)?

Thanks

 

[InteGrand]

Hey so I was wondering if anyone could say whether or not I can do the working out that I do for volumes questions...

Eg Q. Consider a shell of inner radius x, outer radius x + δx, and height y.

In textbooks, I see them go: δV=pi( (x+δx)^2 -x^2)y
and then by expanding and 'ignoring' the (δx)^2 term they get: 2pixyδx.

However I have also done working out like this:

r=x, h=y
SA = 2pi*r*h
SA =2pixy
therefore δV=2pixyδx as it is with respect to x.

Am I allowed to do the working out this second way (the way I always do...)?

Thanks

Yes, you should be able to, see the Board of Studies solutions to Q7(a) of the 2011 HSC paper: http://www.boardofstudies.nsw.edu.a...ematics-extension-2-hsc-sample-answers-11.pdf

(Here's the paper: http://www.boardofstudies.nsw.edu.a...ms/pdf_doc/2011-hsc-exam-mathematics-ext2.pdf )

 

[Axio]

Yes, you should be able to, see the Board of Studies solutions to Q7(a) of the 2011 HSC paper: http://www.boardofstudies.nsw.edu.a...ematics-extension-2-hsc-sample-answers-11.pdf

(Here's the paper: http://www.boardofstudies.nsw.edu.a...ms/pdf_doc/2011-hsc-exam-mathematics-ext2.pdf )

Thanks!