What is the volume of the solid of revolution generated by revolving the area bounded by y = 2, y = x+3 and x = 4 around the x-axis

- anonymous

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- amistre64

ahhh volume of solids :) nice

- amistre64

isnt that just a cone?

- anonymous

Lol - up for helping me out one more time?

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## More answers

- amistre64

spin this right?

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- amistre64

it amounts to a cylinder and a cone :)

- anonymous

Yes, that's the same sketch I made

- anonymous

Lol

- amistre64

y = 2 when x = -1; -1 to 4 is 5 units;
area of the left part is 5(pi) 2^2

- amistre64

20 pi is the area of the "cylindar";
now add the cone...

- amistre64

we have a base area of pi 2^2 = 4pi; and a height from -1 to -3 = 2

- amistre64

4pi(2)
----- = 8pi/3 add the other
3
8pi + 60pi
--------- = 68pi/3
3

- amistre64

thats my guess :) cone plus cylinder = total;

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- myininaya

this might be wrong but I have to leave

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- amistre64

that might be right :)

- anonymous

hmm -

- amistre64

we can solve both ways ;)

- myininaya

you guys have fun i have a date lol

- amistre64

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- anonymous

hmm - i'm not sure if 68pi/3 is right

- amistre64

we move everything to the right by 1 to get bounbes from 0 to 5; then rotate the triangle in a torus

- anonymous

It was a multiple choice question from the book - but no answer in the back to confirm

- amistre64

\[\pi \int\limits_{0}^{5} [f(x)]^2 dx\]

- amistre64

y=x+3 when moved to the right by 1 becomes:
y+1 = x+3
y = x+2
integrate (x+2)^2

- amistre64

(x+2)^3
------- = F(x); play with the 5 and we get... 343pi/3
3

- anonymous

the numerator seems to be off - it's either 14 pi, 275 pi or 140 pi

- anonymous

I can't seem to get any of those numbers on accident either!

- amistre64

lets see if I integrated it forrectly :)
u = x+2; du = dx
[S] u^2 du -> (u^3)/3 = (x+2)^3/3 thats right....

- amistre64

its from 0 to 5 so..... thats where I misssed it lol
pi(343-8)/3

- amistre64

i assumed 0 was just 0

- amistre64

we have to subtract something; the area of the cylindar beneath it.....

- amistre64

we made a solid and forgot to ...by we I mean me lol..... forgot to take away the solid formed beneath it

- anonymous

lol

- amistre64

subtract another 20pi

- amistre64

pi(343-68)/3
275pi/3

- anonymous

Great! Glad we (I mean you) could figure it out and explain it to me! Lol

- amistre64

lol.... i took the whole thing and forgot to cut out the center of the doughnot.... that was my error the first go araound

- anonymous

No worries!! I'm glad you could figure it out!

- anonymous

I appreciate the help very much! I may post a few more if you're still around!

- amistre64

this is the visual lol

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- amistre64

i gotsta take a macroeconomics final so good luck ;)

- anonymous

Ahh! Haha

- anonymous

Good luck!

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