need a bit of help setting this up.

Find the volume of the ellipsoid x^2+y^2+9z^2=64.

i know the volume is gonna be 4/3 pi r^3 and r here is 8

Question

need a bit of help setting this up.  

Find the volume of the ellipsoid x^2+y^2+9z^2=64.

i know the volume is gonna be 4/3 pi r^3 and r here is 8

anonymous · Answer

Wow....I am so bad at this. sorry!

anonymous · Answer

that's ok, @PaulaLovesSchool13, i appreciate you taking the time to look and try.  :D

zpupster · Answer

On the x-axis: For this case, y = z = 0, so we have x^2 = 64 and x = +or- 8. The distance from the center of the ellipsoid to either endpoint on the x axis is 8 

On the y-axis: For this case, x = z = 0
y^2 = 64 so y = +or- 8

On the z-axis: For this case, x = y = 0
z^2= 64/9
z=8/3


so V=(4/3pi)(8)(8)(8/3)

anonymous · Answer

so we don't have to integrate for this?  it's just as easy as that?

ikram002p · Answer

double integrate

ganeshie8 · Answer

familiar with change of vairables and jacobians ?

anonymous · Answer

jacobi what now?

anonymous · Answer

i know this is from the polar integrals section.  never heard of that word

ganeshie8 · Answer

x^2+y^2+9z^2=64

(x/8)^2 + (y/8)^2 + (3z/8)^2 = 1

ganeshie8 · Answer

Oh you want to work it using a double integral is it ?

anonymous · Answer

well, zpupster had the right answer and that made sense to me, but i guess we're supposed to do it integrating.  not sure why....more complicated that way.

ganeshie8 · Answer

zpupster has just used the volume of ellipsoid formula : $\large  \frac{4}{3}abc$

ganeshie8 · Answer

$\large \frac{4\pi}{3}abc$

ganeshie8 · Answer

is this question from calc or geometry ?

anonymous · Answer

calc 3.  polar integrals

ganeshie8 · Answer

double integrals / triple integrals ?

anonymous · Answer

either or.  we've touched on triple.

ganeshie8 · Answer

good, then try setting up a triple integral

ganeshie8 · Answer

have they covered Jacobians yet ?

anonymous · Answer

no.

anonymous · Answer

brb.

anonymous · Answer

.....

ganeshie8 · Answer

it would be complicated without  change of variables hmm

zpupster · Answer

wish i could help more i can understand the idea behind it but i can not explain it here are a couple of articles that may help you in understanding the triple integration as a solution for Volume of ellipsoid here is a tripe integral solution https://answers.yahoo.com/question/index?qid=20091010165412AArnjUe and here is a proof of the formula http://www.math24.net/calculation-of-volumes-using-triple-integrals.html

anonymous · Answer

ok.  i'm just gonna move on to the next problem and talk to the teacher today.  thanks for the help, guys.