Q7 (a) Volumes 4 Marker --> will I get 4/4? (1 Viewer)

cssftw · Oct 26, 2011

Here was my working out:

$A(x)=2\pi rh\\\\r=1-x\\\\h=y\\\\\therefore h=\frac{x}{1+x^2}\\\\\therefore A(x)=2\pi (1-x)(\frac{x}{1+x^2})\\\\\therefore \Delta V=2\pi(\frac{x}{1+x^2}-\frac{x^2}{1+x^2}).\: \Delta x\\\\\therefore V=\lim_{\Delta x \to 0}\sum_{x=0}^{1}2\pi(\frac{x}{1+x^2}-\frac{x^2}{1+x^2}).\Delta x\\\\\therefore V=2\pi\int_{0}^{1}\frac{x}{1+x^2}-\frac{x^2}{1+x^2}\: dx\\\\\therefore V=2\pi[\frac{1}{2}\ln (1+x^2) -x+\tan^{-1}x]\;0<x<1\\\\\therefore V=2\pi(\frac{1}{2}\ln (2) - 1 + \frac{\pi}{4})\;\;\; \; units^3$

I know it seems like a lot of working out but I'm pretty sure in the exam, I skipped a few steps and it was like 5-6 lines of working out total --> Is this enough to get 4/4? 4/4 was a lot of marks for a volumes question....

also I heard some people did some crap like include + (delta(x)) as part of their radius which is the CAMBRIDGE method, and apparently the theoretically correct method. I suppose my method is the cheap easy fast way.

Would I get full marks for this tho? THanks appreciate the help.

Wight · Oct 27, 2011

Someone should probably reply to this lol.
It looks fine imo, exactly the way I did it with the exception of my silly mistakes where, for some reason, my radius of 1-x suddenly became x in my integral for some odd reason...there goes 4 marks for me

.

Basically you note cylindrical shells with the 2pirh.
You correctly evaluate r and h.
You determine the integral.
And you solve the integral.

So it should be fine.
I haven't looked at terry lee solutions. So if you haven't done so, which I doubt, check them.

(I love resurrecting aging threads, loljk just wanted my post count to hit 50 before I go to bed)

cutemouse · Oct 27, 2011

Well this is the method that Coroneos uses in his book... so I'd say that it's correct...

Username2 · Oct 27, 2011

Sorry if this is hijacking the thread but is it really likely that I'll lose all 4 marks if I rotated it around the wrong line (like a massive idiot may i add)?

Studymates · Oct 27, 2011

Username2 said:
Sorry if this is hijacking the thread but is it really likely that I'll lose all 4 marks if I rotated it around the wrong line (like a massive idiot may i add)?

u will lose maybe like 2-3 depends on the markers mood
if he sees potential then u will lose 2 only but otherwise if he thinks u took the easier option ull lose 3 but u wont lose all 4

D94 · Oct 27, 2011

Studymates said:
u will lose maybe like 2-3 depends on the markers mood
if he sees potential then u will lose 2 only but otherwise if he thinks u took the easier option ull lose 3 but u wont lose all 4

They mark on method. Username2 will lose only 1 mark if the method is correct. To be fair, volumes are pretty easy, and it's just repeating the same steps again and again. If the correct method is there, then he will lose 1 mark for the initial mistake, and everything follows as normal marking.

And to confirm this, this was the marking criteria for 2010's cylindrical shells question:

Correct solution (4)
Obtains a correct primitive (3)
Obtains a correct integral (2)
Makes progress towards obtaining a correct integral (1)

So Username2 has achieved all but the "correct solution" part. Note "a correct..." is different to "the correct...", hence losing only 1 mark, assuming all other working out is correct.

Official · Oct 27, 2011

cssftw said:
Here was my working out:

$A(x)=2\pi rh\\\\r=1-x\\\\h=y\\\\\therefore h=\frac{x}{1+x^2}\\\\\therefore A(x)=2\pi (1-x)(\frac{x}{1+x^2})\\\\\therefore \Delta V=2\pi(\frac{x}{1+x^2}-\frac{x^2}{1+x^2}).\: \Delta x\\\\\therefore V=\lim_{\Delta x \to 0}\sum_{x=0}^{1}2\pi(\frac{x}{1+x^2}-\frac{x^2}{1+x^2}).\Delta x\\\\\therefore V=2\pi\int_{0}^{1}\frac{x}{1+x^2}-\frac{x^2}{1+x^2}\: dx\\\\\therefore V=2\pi[\frac{1}{2}\ln (1+x^2) -x+\tan^{-1}x]\;0<x<1\\\\\therefore V=2\pi(\frac{1}{2}\ln (2) - 1 + \frac{\pi}{4})\;\;\; \; units^3$

I know it seems like a lot of working out but I'm pretty sure in the exam, I skipped a few steps and it was like 5-6 lines of working out total --> Is this enough to get 4/4? 4/4 was a lot of marks for a volumes question....

also I heard some people did some crap like include + (delta(x)) as part of their radius which is the CAMBRIDGE method, and apparently the theoretically correct method. I suppose my method is the cheap easy fast way.

Would I get full marks for this tho? THanks appreciate the help.

easy 4/4 lol, you are allowed to skip all +delta x stuff

you can start with dv = 2pixy dx

markrule5 · Oct 28, 2011

OMG i got the exact same answer , i think u would get 4/4
but i rotated it around the x-axis and took the dx instead of dy two wrong things ffs but it still worked out i dunno how

Q7 (a) Volumes 4 Marker --> will I get 4/4? (1 Viewer)

cssftw

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Wight

ಠ_ಠ

cutemouse

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Username2

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Studymates

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D94

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Official

Bring it on

markrule5

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