## xRAWRRx3 3 years ago Please help. :( In the figure below, rectangle ABCD is rotated about side AB. If Ab = 10 and BC = 4 , what is the volume of the resulting solid?

1. xRAWRRx3

|dw:1338516177766:dw|

2. jim_thompson5910

First, it helps to figure out what solid figure you'll get if you rotate this

3. jim_thompson5910

Any ideas of what type of solid figure it will be?

4. xRAWRRx3

i have no clue.

5. jim_thompson5910

Imagine spinning this around AB (think of AB as stuck to the ground) and this rectangle is like a door. What you'll get is a cylinder.

6. xRAWRRx3

How'd you get that? Is that like common sense or something?

7. jim_thompson5910

I'm imagining it in my mind really, but you can grab a rectangular object and spin it along a side. You'll see that it traces out a cylinder.

8. xRAWRRx3

then i guess by rotates they mean folded kinda??

9. xRAWRRx3

**rotated

10. xRAWRRx3

like rolled up?

11. jim_thompson5910

no it's not folding in any way

12. jim_thompson5910

one moment while I track down an animation of this

13. xRAWRRx3

okay, thank you.

14. jim_thompson5910

15. xRAWRRx3

It's alright. I got it. so what do i do after?

16. jim_thompson5910

When it's not moving, it's in one spot...but when it spins, it resembles a circle correct?

17. xRAWRRx3

Oh. Okay. So its a cyclinder. what do i do after?

18. jim_thompson5910

what's the height of the cylinder?

19. xRAWRRx3

10.

20. jim_thompson5910

and what's the radius of the top of the cylinder?

21. xRAWRRx3

but isn't the circumference 4?

22. xRAWRRx3

since the whole side BC is 4?

23. jim_thompson5910

that's not the circumference

24. jim_thompson5910

that's actually the radius since that's as far as it goes in that direction

25. jim_thompson5910

|dw:1338517802914:dw|

26. jim_thompson5910

|dw:1338517841316:dw|

27. jim_thompson5910

The rectangle will rotate about that dotted line (which is AB) to create that cylinder. So that's why the radius is 4.

28. xRAWRRx3

I don't really get how its four...

29. jim_thompson5910

Do you see how that cylinder is created?

30. xRAWRRx3

how'd you get it? i still dont get how you created the cylinder like that..

31. jim_thompson5910

I spun the rectangle around that dotted line. The cylinder represents the space that the rectangle carves out (think of the spinning rectangle as a saw or drill cutting into wood)

32. xRAWRRx3

but how is the radius 4? wouldn't it be 2?

33. jim_thompson5910

no, the radius is shown in the next drawing |dw:1338519158344:dw|

34. jim_thompson5910

and that length is exactly the length of BC

35. xRAWRRx3

oh, so AB stays in one spot and The rest of the rectangle kinda like spun around to make the cylinder?

36. jim_thompson5910

exactly, AB never move at all but the other points spin/move around

37. jim_thompson5910

A and B never move as well

38. xRAWRRx3

ohhh, i get it. so is the answer 160 pi?

39. jim_thompson5910

you nailed it

40. xRAWRRx3

Yay :) thank you so much x)

41. jim_thompson5910

you're welcome