Volumes (1 Viewer)

[Premus]

Hi

just want to confirm something...
for finding volumes using cylindrical shells, do we need to show the entire working in the HSC exam, ie
V =integral pi h (R^2 - r^2) , and then simplify that.

or can we do it the short way , V = integral 2pi (Shell radius) ( Shell Height) ?


Thanks

 

[Jase]

You would usually need to show it, at least, thats the safe way.
But if you do it that way, make sure you write the as the first line:

deltaV = lim {delta x -> 0} Sigma e.t.c

 

[mojako]

I think more recently there has been a move towards the practical way:
V = integral 2pi (Shell radius) ( Shell Height)

EDIT:
Can someone call the HSC advice line?
Or should I call myself? hmm.....

 

[CrashOveride]

ok waht ive been the whole time and ive noticed most solutions just get the area of the strip and then just integrate that and ur done.

 

[CrashOveride]

ok its ok to do what i said...they do the same thing in MANSW

 

[CrashOveride]

You would usually need to show it, at least, thats the safe way.
But if you do it that way, make sure you write the as the first line:

deltaV = lim {delta x -> 0} Sigma e.t.c

V not deltaV ^^

 

[BillyMak]

I've been taught to do it from the very start, ie. Draw a diagram, indicate the region that is being rotated, draw up a rectangle inside the graph, label the length and height (as deltaX and Y, or whatever the question requires)
Then draw a cilindrical shell indicating where it has been taken from the graph, and then a stretched out rectangular prism so the marker knows that you know what you're talking about.

Is this too much?

 

[mojako]

So in other words you're just using V = integral 2pi (Shell radius) ( Shell Height) right?

If you do the derivation you should not draw the stretched out rectangular prism as it is irrelevant to the derivation process.

In fact it's contradictory to your working because using the full derivation process you're not cutting the shell and stretching it out.
(but you're ignoring dx^2 which I guess is identical to cutting the shell)