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 August 24th, 2019, 03:25 PM #2 Math Team     Joined: Jul 2011 From: Texas Posts: 3,016 Thanks: 1600 Second theorem of Pappus ...
 August 24th, 2019, 03:47 PM #3 Member   Joined: May 2018 From: Idaho, USA Posts: 65 Thanks: 7 @skeeter, thanks for sharing that with me. Is that what this is called? The second theorem of Pappus?
 August 25th, 2019, 04:31 AM #4 Math Team     Joined: Jul 2011 From: Texas Posts: 3,016 Thanks: 1600 Link to the first and second theorems of Pappus ... Pappus's Centroid Theorem -- from Wolfram MathWorld
August 25th, 2019, 04:58 AM   #5
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Quote:
 Originally Posted by jnicholes I turned the larger radius into a cylinder, then found the volume.
Can you give the details of that?

 August 25th, 2019, 07:46 AM #6 Member   Joined: May 2018 From: Idaho, USA Posts: 65 Thanks: 7 @skipjack, sure. Here is what I did. The length from the middle of the torus to the middle of the tube is 3.5. The radius of the tube is 0.5. I did the following with these numbers to turn the larger radius into a cylinder with a 0.5 radius and a 3.5 length. Pi*0.5^2 After that, I multiplied it by the larger radius, 3.5. The radius of the torus is now the volume of a cylinder assuming the radius is a 3d cylinder. Simply multiply that by 2pi and you get the torus volume. Divide it by 4 to get the area I was looking for. Does this explain it well enough? Jared
 August 25th, 2019, 08:47 AM #7 Global Moderator   Joined: Dec 2006 Posts: 20,972 Thanks: 2222 Your first step produced $\pi$0.5². This was presumably based on the formula for the area of a circle, but you didn't mention this circle or why you chose to use it. Your second step was to multiply by the larger radius, 3.5. That doesn't mean that that the multiplier "is now a volume" or "has turned into a cylinder". Rather, you have used it as the length of a cylinder, but why did you choose that particular cylinder? You seem also to have assumed, without saying so, the formula for the volume of a right circular cylinder.
 August 25th, 2019, 10:12 AM #8 Senior Member   Joined: Jun 2019 From: USA Posts: 213 Thanks: 90 The dude correctly deduced the formula for the volume of a torus through visualisation. What are you harping on him for? Thanks from Greens
 August 25th, 2019, 11:55 AM #9 Member   Joined: May 2018 From: Idaho, USA Posts: 65 Thanks: 7 one thing you need to know about me, I think a lot differently than most people. It comes with ADHD. I visualized the whole thing in my head, then I figured it out. Basically, I think in pictures. That plus my calculator. Regardless, I got the same answer as the correct formula. Anyway, just for the record, I don't feel he's getting on my case. I don't feel offense at all. I have an idea that might help explain my method. Just give me some time. Jared
 August 25th, 2019, 12:27 PM #10 Member   Joined: May 2018 From: Idaho, USA Posts: 65 Thanks: 7 I made a video of how I did it with me explaining what I did. I hope this helps! Jared

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