Volumes problem -show area = ... (1 Viewer)

[gracie189]

Question - the region bounded by the curve y = (x-1)(3-x) and the x axis is rotated about the line x = 3 to form a solid.
When the region is rotated, horizontal line segment l at height y sweeps out an annulus.
Show that the area of the annulus A=square root(1-y)

(sorry i dont kno how t put th proper sign in...)

this question was in my last assessment on volumes and integration, which i wont get back until after the holidays (ie, after 24th july)
i couldnt do this problem, and spent two pages scribbling and getting no where.

if someone could explain how its meant to be done, i would really appreciate it
i hate not being able to do something, and this is driving me crazy, cos i have NO IDEA

thnx

 

[xclusv2bhung]

ooh damn i havent studied volumes lately , but .
dont you just apply the shell method ?

sorry if i`m wrong tho
but good luck =)

 

[gracie189]

yeah but isnt the shell method for finding volumes..?
this was only the first half of the question, and you were supposed to find the area of the circular.. well i suppose call it a disc or a washer or whatever..
i still kinda havent got the grasp of the method of shells completely.. we only did volumes starting two weeks before the assessment (and we only have one two hour class a week)

thanks anyway

 

[TesseracT22]

umm about this question are you sure it asks you to show the area is sqrt(1-y),
shouldnt there be a pi in there somewhere?

as for solving this one first you have to rearrange eqn in terms of x i.e. quadratic formula giving you 2 x values.

so the inner radius becomes (3-biggerX) and outer radius becomes (3-smallerX)

then its just some algebra and i think you end up with A=4pi*sqrt(1-y)

 

[gracie189]

umm about this question are you sure it asks you to show the area is sqrt(1-y),
shouldnt there be a pi in there somewhere?

as for solving this one first you have to rearrange eqn in terms of x i.e. quadratic formula giving you 2 x values.

so the inner radius becomes (3-biggerX) and outer radius becomes (3-smallerX)

then its just some algebra and i think you end up with A=4pi*sqrt(1-y)

thankyou =) that makes sense..
and yes there was a 4pi in there come to think of it
i must hav accidentaly left it out..

..now i'll go do it agen n make sure i can do it..
i hate not being able to finish questions, or find teh right answer... it drives me crazy... and yeh... i dnt get this paper back till afta th hols, n didnt want it t b driving me insane the whole time lol


thanks so much