xRAWRRx3
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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xRAWRRx3
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|dw:1338516177766:dw|
jim_thompson5910
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First, it helps to figure out what solid figure you'll get if you rotate this
jim_thompson5910
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Any ideas of what type of solid figure it will be?
xRAWRRx3
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i have no clue.
jim_thompson5910
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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.
xRAWRRx3
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How'd you get that? Is that like common sense or something?
jim_thompson5910
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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.
xRAWRRx3
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then i guess by rotates they mean folded kinda??
xRAWRRx3
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**rotated
xRAWRRx3
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like rolled up?
jim_thompson5910
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no it's not folding in any way
jim_thompson5910
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one moment while I track down an animation of this
xRAWRRx3
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okay, thank you.
jim_thompson5910
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hmm not finding much sadly, but think of a propeller blade
xRAWRRx3
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It's alright. I got it. so what do i do after?
jim_thompson5910
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When it's not moving, it's in one spot...but when it spins, it resembles a circle correct?
xRAWRRx3
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Oh. Okay. So its a cyclinder. what do i do after?
jim_thompson5910
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what's the height of the cylinder?
xRAWRRx3
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10.
jim_thompson5910
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and what's the radius of the top of the cylinder?
xRAWRRx3
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but isn't the circumference 4?
xRAWRRx3
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since the whole side BC is 4?
jim_thompson5910
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that's not the circumference
jim_thompson5910
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that's actually the radius since that's as far as it goes in that direction
jim_thompson5910
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|dw:1338517802914:dw|
jim_thompson5910
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|dw:1338517841316:dw|
jim_thompson5910
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The rectangle will rotate about that dotted line (which is AB) to create that cylinder. So that's why the radius is 4.
xRAWRRx3
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I don't really get how its four...
jim_thompson5910
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Do you see how that cylinder is created?
xRAWRRx3
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how'd you get it? i still dont get how you created the cylinder like that..
jim_thompson5910
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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)
xRAWRRx3
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but how is the radius 4? wouldn't it be 2?
jim_thompson5910
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no, the radius is shown in the next drawing
|dw:1338519158344:dw|
jim_thompson5910
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and that length is exactly the length of BC
xRAWRRx3
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oh, so AB stays in one spot and The rest of the rectangle kinda like spun around to make the cylinder?
jim_thompson5910
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exactly, AB never move at all but the other points spin/move around
jim_thompson5910
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A and B never move as well
xRAWRRx3
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ohhh, i get it. so is the answer 160 pi?
jim_thompson5910
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you nailed it
xRAWRRx3
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Yay :) thank you so much x)
jim_thompson5910
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you're welcome