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## anonymous one year ago Suppose R is the region bounded by y = x^2, x = 2, and y = 0. A solid is generated by revolving R about the x = 3. Find the volume of the solid. 8/3π (18-8√2)π 8π 12π No idea how to do this, any help is appreciated thanks!

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1. dan815

|dw:1435372707180:dw|

2. dan815

|dw:1435372819291:dw|

3. dan815

|dw:1435372964110:dw|

4. dan815

|dw:1435373065795:dw|

5. dan815

does this make sense?

6. dan815

you should probably draw these rectangles vertically so u can integrate wrt to x and your integral looks better

7. dan815

|dw:1435373229140:dw|

8. dan815

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9. dan815

each of those rectangles gives u a mini ring

10. dan815

you add the volume of all the mini rings

11. dan815

solve it

12. dan815

you there @sun__chips

13. dan815

i hope the pictures didnt confuse you, the basic idea of what im doing is simple it just looks a bit confusing all written out like this, what we are doing is looking at each rectangle and revolving each one, around x=3 axis

14. dan815

|dw:1435373637040:dw|

15. dan815

you can cut this thing somewhere and it will look just like a 3D volume thing like this

16. dan815

|dw:1435373725195:dw|

17. dan815

where the height of this thing is 2pir

18. dan815

|dw:1435373793422:dw|

19. dan815

thats kind of cool actually

20. dan815

here is something interesting

21. dan815

a trinagle volume rotated must be equal to some rectangle rotated, where the height of the rectangle is the average height of the triangle

22. dan815

|dw:1435373966303:dw|

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