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Can you help me , please?

  • Thread starter vip89
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  • #1
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Can you help me , please??

Can you solve this problem by using Calculus l "" Volumes by Slicing and Rotation About an Axis"" ??
Develop a formula for the volume of an ellipsoid of the form

( x^2/a^2)+(y^2/b^2)+(z^2/c^2)=1, a, b, c > 0.

I want the steps , because I know the final answer .
 

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  • #2
tiny-tim
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Welcome to PF!

Hi vip89! Welcome to PF! :smile:

Show us what you've tried, and where you're stuck, and then we'll know how to help you! :smile:
 
  • #3
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I know that I must sketch,find the equation of the cross section , find the area from A=piab and x^2/a^2+y^2/b^2=1
Finally,I must find the definit integral of the area
the final answer will be 4pi/3 abc
 
  • #4
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I dont know how to do this , and how to apply my steps?!
 
  • #5
tiny-tim
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Hi vip89! :smile:
I know that I must sketch,find the equation of the cross section …
ok … we usually take horizontal cross-sections (don't have to) …

in other words, the intersection with a plane z = constant.

So what is the equation (in x and y) if you put z = w (a constant) … ? :smile:

… and then what is the area? :smile:
 
  • #6
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thnkx very much
 
  • #7
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I trid to solve it by this way,but strang things will appear,the equation be more complicated!!
 
  • #8
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Show us your work. You can either take a picture, scan it, and upload it, or you can try using LaTeX in between [noparse][tex] and [/tex][/noparse] tags.
 
  • #9
tiny-tim
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I trid to solve it by this way,but strang things will appear,the equation be more complicated!!
Hi vip89! :smile:

Show us how far you got …

What equation (in x and y) did you get for the horizontal cross-sections when you put z = w (a constant)? :smile:
 
  • #10
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I want the steps , because I know the final answer .
AND WE WANT YOUR WORK!!!

lol ... funny kid we're not here to do your hw
 
  • #11
tiny-tim
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Welcome to this thread, rocomath!

oi … rocomath! … that was vip89's very first post (seven days ago)!

… but he's getting the hang of it now! :smile:

If you can't help, just say "welcome!" :smile:
 
  • #12
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oi … rocomath! … that was vip89's very first post (seven days ago)!

… but he's getting the hang of it now! :smile:

If you can't help, just say "welcome!" :smile:
sorry :( i've grown less tolerant towards ppl just wanting us to do their hw.
 
  • #13
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These are my trials
I have the idea but cant get the right answer
pls reply
THNKX
 

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  • #14
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Continue:
 

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  • #15
HallsofIvy
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In your first sheet, you start with [tex]\int A(x)dx[/tex] and then immediately switch to [tex]\int x y[/itex] without a "dx" at all. How did that happen? I also cannot see any good reason for writing x as a function of y and z and writing y as a function of x and z.
You are correct that [tex]y= b\sqrt{1- x^/a^2- z^2/c^2}[/tex] and that [tex]z= c\sqrt{1- x^2/a^2- y^2/b^2[/tex]. The first tells you that when z= 0, [tex]y= b\sqrt{1- x^2/a^2}[/tex] and the second tells you that when y= 0, [tex]z= c\sqrt{1- x^2/a^2}[/tex]. In other words, at each x, the cross section is an ellipse with semi-axes [tex]b\sqrt{1-x^2/a^2}[/tex] and [tex]c\sqrt{1- x^2/a^2}[/tex]. Do you know that the area of an ellipse with semi-axes a and b is [tex]\pi ab[/tex]?
 
  • #16
tiny-tim
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hmm … let's start at the top of your page 3 …
w² = (1 - x²/a² - y²/b²)c²
which I take it is following my suggestion …
So what is the equation (in x and y) if you put z = w (a constant) … ? :smile:

… and then what is the area? :smile:
And then you try to use the formula A = πab for the area of an ellipse.

BUT … that formula only applies if the equation for the ellipse is in the standard form, with nothing but x² and y² on the left and "= 1" on the right.

You must put w² = (1 - x²/a² - y²/b²)c² into that form first.

Then you will get a "new a and b" that are not the same as the original a and b.

ok … rearrange w² = (1 - x²/a² - y²/b²)c² into the standard form … and then find the area. :smile:
 

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