Volumes - Slicing (1 Viewer)

[haboozin]

hey,

I came along this question. Did it... looked at the solution and they do it differently.
I dont know why they do that and they get a different answer.

So i'll see what you guys get..
I'm pretty sure mine is right

 

[KFunk]

Did you get anything in the realms of 2547a³π/20 units cubed? I banged that up pretty quickly so chances are it's wrong but if not let me know and I'll type up any part of the solution that you're after.

 

[serge]

did anyone get an answer with 3 different powers of a?

 

[haboozin]

did anyone get an answer with 3 different powers of a?

definatly not...

 

[haboozin]

Did you get anything in the realms of 2547a³π/20 units cubed? I banged that up pretty quickly so chances are it's wrong but if not let me know and I'll type up any part of the solution that you're after.

my answer is (around) ... half of yours

the answer they gave... much smaller.

i dont think they're right


This is what they do:

(R - r)^2

and it really bothers me, it should be R^2 - r^2

 

[serge]

do they have any working? what book's it from

 

[serge]

it's slicing why would your method be correct?

it looks like you're trying to rotate it around something...

post the answer they give

 

[haboozin]

it's slicing why would your method be correct?

it looks like you're trying to rotate it around something...

slicing is a method of finding a volume...


a volume is achieved by the shaded area being rotated?

stop confusing me... stressful times

 

[robbo_145]

i get (9πa²)/4

not sure if im reading the question right though :/

 

[serge]

slicing is a method of finding a volume...


a volume is achieved by the shaded area being rotated?

stop confusing me... stressful times

yeh, my bad

i mean it is a plane question,
I didnt know you could get those by rotating

 

[haboozin]

i get (9πa²)/4

not sure if im reading the question right though :/

sorry cant be, look at Kfunk's... should be close to that. (or even that)

 

[serge]

the way i see it, is you dont need to rotate it

Area of the slice= 1/2.Pi.r^2

r=1/2[ (4ax)^1/2 - 2/3x]... but that just gets ugly

then integrate the area for volume

 

[KFunk]

my answer is (around) ... half of yours

the answer they gave... much smaller.

i dont think they're right


This is what they do:

(R - r)^2

and it really bothers me, it should be R^2 - r^2

They're the curves y = 2√(ax) and y = 2x/3 right? So the radius of each semi-circle is r = (√(ax) - x/3).

The volume should then be π/2 ∑ r² δx from 0 to 9a as δx-->0

= 2547a³π/20

Anything wrong with that reasoning?

 

[KFunk]

the way i see it, is you dont need to rotate it

Whether or not that method is a rotation is more of a conceptual issue.

 

[robbo_145]

woops forgot to square. my revised answer = (27a³π )/20

 

[serge]

post the book's answer (even if you think it's wrong)

 

[serge]

r = (√(ax) - x/3).


Anything wrong with that reasoning?

i think, when you square your radius you're integral has more than
1 power of a?

might be doing it wrong

 

[KFunk]

i think, when you square your radius you're integral has more than
1 power of a?

might be doing it wrong

It works out I think:

ax + x²/9 - (2√a/3)x^3/2 ... integrate

[(ax²)/2 + x³/27 - (4√a/15)x^5/2] from 0 to 9a.

[81a³/2 + 27a³ - 972a³/15]

The limits include an 'a' term so everything evens out to leave a³.

 

[serge]

thats cool thanks

 

[KFunk]

And it looks like I can't add numbers together . My previously posted answer of 2547a²π/20 should probably be 27a³π/20 , that is, if I even added it up correctly this time.