Theorem of Pappas (volumes) (1 Viewer)

[tiggerfamilytre]

just wondering if anyone knows whether or not this is accepted in the HSC, because it makes things a lot easier sometimes. It goes something like 'if a plane of area A is rotated around an axis R [where the axis does not cut the area] then the volume is given by V = 2piRA'. Note this only applys to an area that is symmetrical about the axis parallel to the axis of rotation. An example where it might be useful is from the HSC 1995, where you are asked to find the volume of the solid formed when the circle x^2 + y^2 = 16 is rotated around the line x = 9. By the theorem of Pappas, Volume = 2pi(9)(16pi) = 288pi^2 cubic units.

 

[wanton-wonton]

just wondering if anyone knows whether or not this is accepted in the HSC, because it makes things a lot easier sometimes. It goes something like 'if a plane of area A is rotated around an axis R [where the axis does not cut the area] then the volume is given by V = 2piRA'. Note this only applys to an area that is symmetrical about the axis parallel to the axis of rotation. An example where it might be useful is from the HSC 1995, where you are asked to find the volume of the solid formed when the circle x^2 + y^2 = 16 is rotated around the line x = 9. By the theorem of Pappas, Volume = 2pi(9)(16pi) = 288pi^2 cubic units.

Yes, it would work well for the torus questions, but usually the question would specify what method to use, that is, shells or slices.

 

[Slidey]

Not allowed to use Pappas' theorem in HSC.

 

[wanton-wonton]

Not allowed to use Pappas' theorem in HSC.

But if they don't specify (which they usually do), why not. You know, it'd be a great way to check your answer.

 

[Slidey]

Check your answer, sure. But it shouldn't be your solution (unless it is a last resort).

 

[wanton-wonton]

Check your answer, sure. But it shouldn't be your solution (unless it is a last resort).

But the whole purpose of Maths is to make life simple. I think in an school exam, unless you've been asked to use slices/shells, then you can use the theorem. You can argue your way through it, since they don't specify which method to use and it just makes life a whole lot simpler.

And with the marks allocation to a Volumes question, as long as the get the answer right showing relevant working, you should get the full marks.

Having said that, I wouldn't risk something like that in an HSC exam, since you can't really argue with the examiner.

 

[Slidey]

But the whole purpose of Maths is to make life simple.

And the whole purpose of the HSC is to make life harder.

My teacher dislikes me using the 'otherwise' approaches, but that is all. In the case of Pappas' theorem he explicitly told me only to use it to check my answer. *shrug*

 

[SeDaTeD]

If I recall correctly, Theorem of Pappus says more generally: the volume is equal to the area of the region times the distance travelled by the centre of mass of the region. ie. 2piRA, with R being the distance from the axis to the centre of mass. The region must not intersect the axis of course.

 

[casebash]

Hey, we at Ruse were taught that we could use this in the HSC.

 

[wanton-wonton]

Hey, we at Ruse were taught that we could use this in the HSC.

I know your tricks, you just want to fuck up other people's HSC, isn't that right.

 

[adzy]

Just curious, if given a function and x value, is it possible to work out the centre of mass? Sounds like some Physics Olympiad knowledge needed.

 

[ngai]

Hey, we at Ruse were taught that we could use this in the HSC.

your teacher said so?
or another teacher?
i suggest u dont use it tho, coz it makes all the donuts a joke
esp if it says its worth like 5 marks and u write one line...

 

[SeDaTeD]

Well, perhaps I should say the centroid instead, that removes any required physics principles.

 

[dawso]

if the question says..."find the volume" then ur correct, normally it says, shwo the volume is given by this integral....hence find the volume, or specifies the method or such, then u cant use it