Volumes of solids of revolution

[stonecold]

Ohhh... right.. I shaded in the blue part and half of the green part :| I got it confused with the ares with the y-axis then?

So basically for this question I just calculate the area bound between x=1 and x=4... wait is the green supposed to be pink in the above diagram?

No, it is right.

Have you done anulus' yet?

[Andiio]

Ohhh... right.. I shaded in the blue part and half of the green part :| I got it confused with the ares with the y-axis then?

So basically for this question I just calculate the area bound between x=1 and x=4... wait is the green supposed to be pink in the above diagram?

No, it is right.

Have you done anulus' yet?

Am I right in saying that we just want the area the curve makes with the x-axis? i.e. the area below the curve?

Never heard of that anulus' :\ what are they?

[stonecold]

Ohhh... right.. I shaded in the blue part and half of the green part :| I got it confused with the ares with the y-axis then?

So basically for this question I just calculate the area bound between x=1 and x=4... wait is the green supposed to be pink in the above diagram?

No, it is right.

Have you done anulus' yet?

Am I right in saying that we just want the area the curve makes with the x-axis? i.e. the area below the curve?

Never heard of that anulus' :\ what are they?

Firstly, I should spell it correctly lol.  Annuli (Annulus sing.)  are basically washers.  They are a type of solid of revolution, but when you do your revolution around the axis, you get a hole in the middle, creating a washer type solid, for which the technical term is 'annulus.'

Can you see how if you revolve that pink shaded area around the y-axis, you create a solid with a hole in the middle?

To overcome this in your calculations, you still use

V=pi x r^2 x thickness

however now r^2= r^2 outer curve - r^2 inner curve.

I can post up a full solution tomorrow night if you can be bothered waiting.  

Edit: And to answer your question, yes, you do want the area under between x=1, x=4 and the x-axis, but then you have to revolve this around the y-axis and find the volume.

[Andiio]

Ohhh... right.. I shaded in the blue part and half of the green part :| I got it confused with the ares with the y-axis then?

So basically for this question I just calculate the area bound between x=1 and x=4... wait is the green supposed to be pink in the above diagram?

No, it is right.

Have you done anulus' yet?

Am I right in saying that we just want the area the curve makes with the x-axis? i.e. the area below the curve?

Never heard of that anulus' :\ what are they?

Firstly, I should spell it correctly lol.  Annuli (Annulus sing.)  are basically washers.  They are a type of solid of revolution, but when you do your revolution around the axis, you get a hole in the middle, creating a washer type solid, for which the technical term is 'annulus.'

Can you see how if you revolve that pink shaded area around the y-axis, you create a solid with a hole in the middle?

To overcome this in your calculations, you still use

V=pi x r^2 x thickness

however now r^2= r^2 outer curve - r^2 inner curve.

I can post up a full solution tomorrow night if you can be bothered waiting. 

Ahhh okay yeah I see how that works. Just wondering though, is it a specific topic in the VCE syllabus or are we meant to just deduce it logically?
Haha yes please, that'd be great. I think I'm still a tad sketchy over the areas and all.. :\

[stonecold]

^yeah, it is in your textbook.  i just checked.  that very last formula in the chapter summary of chapter 6 is what you need to know, but in typical vce textbook style, it is explained like a dog's breakfast.

[taiga]

We were taught to deduce it logically though Andiio

[Lols123]

how do you tell what shape something is if they give you a shaded area

[Andiio]

Just wondering, how exactly do you determine the curve that is 'the most to the right' and the curve that is 'the most to the left'?

Is it just the comparison of the x-values between the certain bounds given?

E.g. y=x^2, y=-x from x=0 to x=1

[luffy]

Just wondering, how exactly do you determine the curve that is 'the most to the right' and the curve that is 'the most to the left'?

Is it just the comparison of the x-values between the certain bounds given?

E.g. y=x^2, y=-x from x=0 to x=1

Depends, are you rotating it in the x-axis? or the y-axis?

If by "most to the right" and "most to the left", you are questioning which one to subtract from the other in the integral, I don't use a set rule. Instead, I simply visualise the 3D object produced and "subtract the unwanted area from the total area" and the rest becomes relatively simple.

Sorry - don't think I explained it properly. Hope I helped...

[Andiio]

Is the 'shell method' within the VCE syllabus? Also, in what situations do you use the 'shell' method?

Edit: Is it accepted as formal working out?

[vea]

Is the 'shell method' within the VCE syllabus? Also, in what situations do you use the 'shell' method?

Oh god, Dr He