## anonymous 5 years ago 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

1. amistre64

ahhh volume of solids :) nice

2. amistre64

isnt that just a cone?

3. anonymous

Lol - up for helping me out one more time?

4. amistre64

spin this right?

5. amistre64

it amounts to a cylinder and a cone :)

6. anonymous

Yes, that's the same sketch I made

7. anonymous

Lol

8. amistre64

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

9. amistre64

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

10. amistre64

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

11. amistre64

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

12. amistre64

thats my guess :) cone plus cylinder = total;

13. myininaya

this might be wrong but I have to leave

14. amistre64

that might be right :)

15. anonymous

hmm -

16. amistre64

we can solve both ways ;)

17. myininaya

you guys have fun i have a date lol

18. amistre64

19. anonymous

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

20. amistre64

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

21. anonymous

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

22. amistre64

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

23. amistre64

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

24. amistre64

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

25. anonymous

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

26. anonymous

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

27. 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....

28. amistre64

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

29. amistre64

i assumed 0 was just 0

30. amistre64

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

31. amistre64

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

32. anonymous

lol

33. amistre64

subtract another 20pi

34. amistre64

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

35. anonymous

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

36. 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

37. anonymous

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

38. anonymous

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

39. amistre64

this is the visual lol

40. amistre64

i gotsta take a macroeconomics final so good luck ;)

41. anonymous

Ahh! Haha

42. anonymous

Good luck!