<p>Ok so I'm doing this "horn problem" (that's what the book calls it). It's on page 249 of Calculus Concepts and Applications Second Edition by Paul A. Foerster if anyone has that book.</p>
<p>The question is: Horn Problem: Figure 5-9n shows a horn-shaped solid formed in such a way that a plane perpendicular to the x-axis cuts a circular cross section. Each circle has its center on the graph of y=0.2x^2 and a radius ending on the graph of y=0.16x^2 + 1. Find the volume of the solid if x and y are in centimeters.</p>
<p>Here's a scan of the problem.
<a href="http://putfile.com/pic.php?pic=3/6818034945.jpg&s=x10%5B/url%5D">http://putfile.com/pic.php?pic=3/6818034945.jpg&s=x10</a></p>
<p>I got 8pi/3 as my answer. Two other people I've asked got 5pi/3. It's an even problem so the answer isn't in the back, can someone please figure out this problem?</p>
<p>This is obviously a disk method problem. So we're using pi r^2 to add up al l the cross sections. Diameter is 0.16x^2 +1 minus 0.2x^2, so divide that by 2.</p>
<p>Setting the two equations equal to each other we get x= plus or minus 5. Obviously only x=5 works. </p>
<p>Set up the integral, from 0 to 5, for pi * ((-.04x^2 +1)/2)^2 </p>
<p>which equals 7pi/3.</p>
<p>If you integrate without squaring the radius, you end up with 5pi/3. I'm not sure how you'd get 8pi/3, or was that a typo?</p>
<p>No, based on the graph, the radius r = 0.16x^2 +1 - 0.2 x^2.
Area = pi (integral from 0 to 5 of 0.16x^2 + 1 - 0.2x^2 dx)
= pi (integral from 0 to 5 of 1-0.04x^2 dx)
= pi ( x - 0.04x^3 / 3) from 0 to 5
= pi ( x - x^3 / 75 ) from 0 to 5
= pi ( 5 - 5^3 / 75 - 0)
= pi (10/3) (centimeter, cm)</p>
<p>helllo, you have to square your radius.</p>
<p>My bad, so then you'll get 8pi/3 then</p>
<p>No, 8pi/3 wasn't a typo, that's what I got. So is it really that simple? I thought it was simple as well, but my teacher considered it to be a hard problem, probably because the horn is curved, so I decided to ask here just to make sure.</p>
<p>no, it's just simple like that. 8pi/3</p>
<p>I got 8pi/3 too, orgyjorgy, dont listen to lh0pitalrules, lol jk</p>
<p>ya its definitely 8pi/3, i just did the work</p>
<p>lol, topic's closed!</p>
