the solid lies between planes perpendicular to the x axis at x= - 4 and x = 4. The cross sections perpendicular to the x axis between these planes are squares whose diagonals run from the semicircle y = -sqrt(16 - x^2) to the semicircle y = sqrt(16 - x^2). Find the volume of the described solid.

Question

anonymous · Answer

AP Calculus AB question

anonymous · Answer

I got 512/3, can anyone verify?

anonymous · Answer

|dw:1395375334263:dw|

anonymous · Answer

did I draw it right?

anonymous · Answer

|dw:1395375425066:dw|

anonymous · Answer

okay yes second drawing is what I envisioned, but there isn't a "correct" drawing provided if that's what you're asking

anonymous · Answer

I'll answer in 15 minutes, I have to drive home now :DD

ganeshie8 · Answer

http://www.wolframalpha.com/input/?i=%5Cint_%7B-4%7D%5E4+2%2816-x%5E2%29+dx

anonymous · Answer

thanks both of you!
 ganeshie8 I ended up getting 2(16-x^2) as the area formula and integrating it from -4 to 4 as well. The problem is is that this is a multiple choice question and 512/3 is not an answer choice

ganeshie8 · Answer

^ same answer
you did $\int (side)^2 dx$ righ ?t

ganeshie8 · Answer

okay lets go thru it again

anonymous · Answer

Yes, ∫(side)2dx, given that the side was the diagonal squared times 1/2 and the diagonal was the distance between the functions$$\sqrt{16-x ^{2}}$$ and $$-\sqrt{16-x ^{2}}$$

ganeshie8 · Answer

we're on same page

anonymous · Answer

i think this chalks up to a teacher error, especially since this wasn't the only problem I found with the multiple choice answers. I can't think of a single other way to do the problem