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?

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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?

Mathematics
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|dw:1338516177766:dw|
First, it helps to figure out what solid figure you'll get if you rotate this
Any ideas of what type of solid figure it will be?

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i have no clue.
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.
How'd you get that? Is that like common sense or something?
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.
then i guess by rotates they mean folded kinda??
**rotated
like rolled up?
no it's not folding in any way
one moment while I track down an animation of this
okay, thank you.
hmm not finding much sadly, but think of a propeller blade
It's alright. I got it. so what do i do after?
When it's not moving, it's in one spot...but when it spins, it resembles a circle correct?
Oh. Okay. So its a cyclinder. what do i do after?
what's the height of the cylinder?
10.
and what's the radius of the top of the cylinder?
but isn't the circumference 4?
since the whole side BC is 4?
that's not the circumference
that's actually the radius since that's as far as it goes in that direction
|dw:1338517802914:dw|
|dw:1338517841316:dw|
The rectangle will rotate about that dotted line (which is AB) to create that cylinder. So that's why the radius is 4.
I don't really get how its four...
Do you see how that cylinder is created?
how'd you get it? i still dont get how you created the cylinder like that..
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)
but how is the radius 4? wouldn't it be 2?
no, the radius is shown in the next drawing |dw:1338519158344:dw|
and that length is exactly the length of BC
oh, so AB stays in one spot and The rest of the rectangle kinda like spun around to make the cylinder?
exactly, AB never move at all but the other points spin/move around
A and B never move as well
ohhh, i get it. so is the answer 160 pi?
you nailed it
Yay :) thank you so much x)
you're welcome

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