# Can you help me , please?

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 .

tiny-tim
Homework Helper
Welcome to PF!

Hi vip89! Welcome to PF! Show us what you've tried, and where you're stuck, and then we'll know how to help you! 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

I dont know how to do this , and how to apply my steps?!

tiny-tim
Homework Helper
Hi vip89! 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) … ? … and then what is the area? thnkx very much

I trid to solve it by this way,but strang things will appear,the equation be more complicated!!

Show us your work. You can either take a picture, scan it, and upload it, or you can try using LaTeX in between [noparse]$$and$$[/noparse] tags.

tiny-tim
Homework Helper
I trid to solve it by this way,but strang things will appear,the equation be more complicated!!
Hi vip89! 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)? I want the steps , because I know the final answer .

lol ... funny kid we're not here to do your hw

tiny-tim
Homework Helper

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

… but he's getting the hang of it now! If you can't help, just say "welcome!" oi … rocomath! … that was vip89's very first post (seven days ago)!

… but he's getting the hang of it now! If you can't help, just say "welcome!" sorry :( i've grown less tolerant towards ppl just wanting us to do their hw.

These are my trials
I have the idea but cant get the right answer
THNKX

Continue:

#### Attachments

HallsofIvy
Homework Helper
In your first sheet, you start with $$\int A(x)dx$$ and then immediately switch to $$\int x y[/itex] without a "dx" at all. How did that happen? I also cannot see any good reason for writing x as a function of y and z and writing y as a function of x and z. You are correct that [tex]y= b\sqrt{1- x^/a^2- z^2/c^2}$$ and that $$z= c\sqrt{1- x^2/a^2- y^2/b^2$$. The first tells you that when z= 0, $$y= b\sqrt{1- x^2/a^2}$$ and the second tells you that when y= 0, $$z= c\sqrt{1- x^2/a^2}$$. In other words, at each x, the cross section is an ellipse with semi-axes $$b\sqrt{1-x^2/a^2}$$ and $$c\sqrt{1- x^2/a^2}$$. Do you know that the area of an ellipse with semi-axes a and b is $$\pi ab$$?

tiny-tim
Homework Helper
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) … ? … and then what is the area? 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. 