<p>Good Review Question:
The base of a solid is the region bounded by the parabola x^2 = 8y, and the like y=4, and each cross-section perpendicular to the y-axis is an equilateral triangle. What is the volume of this solid?</p>
<p>make sure you remember that its perpendicular about the y-axis, and that the cross-section is an equilateral triangle?</p>
<p>If you cannot figure it out just post here, and I'll post a detailed solution back ASAP :)</p>
<p>ANOTHER DISGUISED BUMP++</p>
<p>EDIT: ok, to save time here's the solution:
ok, so it says that x^2 = 8y, and y=4, and the area is a triangle equilateral </p>
<p>The area of an equilateral-triangle is side^2 * sqrt(3) / 4..and the side will equal the length of the bounded region (the length of the rectangular sub-interval)...</p>
<p>Now since it says that its about the y-axis I find it easier to convert y in terms of x; so x = +- sqrt(8y), between 0 and 4 (4 because y=4 is now x=4)...</p>
<p>so sqrt(3) / 4 INTEGRATION[from 0 to 4] of (2*sqrt(8y))^2 dy (I said 2 times the square root, because the function is plus and minus[above and below the x-axis] and they are both equal in are so, the length of the box will be the sum of both the areas so 2 ) will yield: **64 * sqrt(3)*</p>
<p>Ah I got it... I was doing it right, but I just made a stupid algebra mistake.</p>
<p>Yet I seem to have used a different method.</p>
<p>I graphed it and saw, again, that it was symmetric around the y-axis. I said that the cross-sectional area was (1/2)(sqrt(8y))(sqrt(8y)*sqrt(3))</p>
<p>(Because x^2 = 8y, and x = sqrt(8y), and the side ratios for the equilateral triangle)</p>
<p>I integrated the area from y=0 to y=4 and got 64*sqrt(3)</p>
<p>^yeah i personally hate these type of questions too...this one is from barrons, and I think is a notch above AP...or maybe it isn't, making such a judgment is what my original topic was about anyway...lol....none-the-less goojob at getting it right</p>
<p>anyone know the answer to my topic's title????????</p>
<p>^ ditto. I've been trying to use Barron's today and when I use it feel stupid, but I'm not doing a bad on the practice AP exams I have... so that's why WE NEED AN ANSWER TO THE THREAD'S QUESTION!</p>
<p>The Barron's book was overall harder than the real test. The questions in the Barron's book were much more tedious and the concepts they tested you on were a bit tougher than the actual test. If you want to be over prepared for the AP exam, use Barron's.</p>
<p>The Princeton Review Book was around the same difficulty as the actual test. I found the multiple choice questions to be the same difficulty and the FRQ a bit easier than the actual test.</p>
<p>As for the BC test it self, the multiple choice was a complete joke. There is nothing tedious in either of the two sections and if you were half-paying attention in class, you should do well on this section. The FRQ I thought was more of a challenge as the concepts were a bit trickier, but not too tough.</p>