<p>it's the area between the circles... doesn't matter where they are.. cause the circles are completley on the right side of y-axis...</p>
<p>i did it and fot 5 pi...</p>
<p>The answer is in fact 40 pi^2. Interesting...</p>
<p>Yup I know what I did, it is 40 pi^2.</p>
<p>Makes sense now.</p>
<p>Oh sweet :)</p>
<p>argh this is going to annoy me now I have to figure it out properly... forgotten all my maths though...</p>
<p>Uh, I dunno if this is wrong, but it gets the right answer, and doesn't use calculus at all, and is pretty easy - Since rings are symmetric about the center, when you rotate the ring about the y-axis, for every point in the ring, there's another point so that when you average the distances when you rotate the points about the y-axis, it's the same as the distance of rotating the center about the y-axis. So it's just the distance of the center rotated about the y-axis times the area of the cross section, or just (2<em>4</em>pi) * (3<em>3</em>pi - 2<em>2</em>pi), or 40pi^2.</p>
<p>Doing math on Christmas Eve....we're all such nerds :)</p>
<p>Nick's method works great. Well done. </p>
<p>Circle 1 rotated forms a cylinder with radius 3 and height 8pi (2 pi 4, the circumference of the torus). Circle 2 rotated forms a cylinder with radius 2 and height 8pi. Hence, the volume of the torus is Volume (Cylinder1) - Volume (Cylinder2). Or</p>
<p>pi (3)^2 8pi - pi (2)^2 8pi
= 72 pi^2 - 32 pi^2
= 40 pi^2</p>