Volumes By shells (1 Viewer)

[tacogym27101990]

hey can someone please help me out with this question?
its Q10 of 6.3 in terry lees book
"the region enclosed by the rhombus ABCD, where A(0,2) B(1,0) C(0,-2) D(-1,0) is rotated about the line x=2 to form a solid. Find the volume"

i broke it up 2 integrals above the x-axis
then found each volume and added them together then doubled it.
and thats the way he did it too, but i think he made a typo on the way

thanks for the help

 

[kooltrainer]

i did a quarter of the diamond then multiplied by 4.. and got the wrong answer... dunno..

 

[tacogym27101990]

yeah you cant do a quarter because the left hand side has a different radius kinda thing
i think

 

[tacogym27101990]

Anyone??
pleaseee

 

[midifile]

Anyone??
pleaseee

I think there is a mistake in the answers. On the right side of pg 364, there is a a line where it says
V= 4pi lim(dx-->0)(1sigma0)(2-x)(2-2x)dx + 4pi lim(dx-->0)(0sigma-1 )(2-x)(2+2x)dx
(d= delta)

I think it should be V= 4pi lim(dx-->0)(1sigma0)(2-x)(2-2x)dx + 4pi lim(dx-->0)(0sigma-1 )(2+x)(2+2x)dx,
because he has split the volume into the right hand side of the y axis and the left hand side of the y axis, but (using cylindrical shells) the left hand side has radius 2+x not 2-x

but im not 100% sure

 

[ngogiathuan]

Yeah im not sure why we have to break the slices into 2 parts (like terry did) either.
I assume they have different radius, but sometimes it doesnt make sense to me.
Can someone explain this? Thanks

 

[conics2008]

try rotating one at a time lol =]

find the equation of the line in the 1st quadrant and the 4th qudrant.. because in quadrant 2 and 3 are parallel to quad 1 and 4 respectivly.

for quad one. the volume is 10pi/3

just find the volumes of each lines etc etc but remember its 2+x and 2+x+dx for quad 3

good luck i cant be stuffed right now.. can you give me the answer.. so i can do this tomorrow at school it looks intresting.