March 15th, 2017, 10:24 PM  #1 
Newbie Joined: Mar 2017 From: Earth Posts: 5 Thanks: 0  volume of this shape
Please I need help to calculate this volume: The base is an ellipse and a/b are its major/minor axes. Thanks. Last edited by skipjack; March 16th, 2017 at 10:22 PM. 
March 16th, 2017, 10:26 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 17,919 Thanks: 1384 
Do you know how to find a volume of revolution?

March 16th, 2017, 11:14 PM  #3 
Newbie Joined: Mar 2017 From: Earth Posts: 5 Thanks: 0 
@skipjack: Yes I know but in this case the base is not a circle it's an ellipse ! I found a solution if x=0 were the "axis of revolution". . But when x=a it's bit tricky....

March 17th, 2017, 01:34 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 17,919 Thanks: 1384 
If the volume for a circular base of radius a is V, the volume for the elliptical base is (b/a)V. The diagram seems poor, as the distance shown as 2$a$ is nothing like twice the distance shown as $a$.

March 17th, 2017, 01:51 AM  #5 
Newbie Joined: Mar 2017 From: Earth Posts: 5 Thanks: 0 
@skipjack : you're right about the diagram  it's just a Paint sketch , it is my mistake. it's to give an idea about the problem...for the volume, I want to find the method/analytical expression not just multiply by b/a. This is the new sketch: Thanks. Last edited by skipjack; August 7th, 2017 at 10:17 PM. 
March 17th, 2017, 02:08 AM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,574 Thanks: 931 Math Focus: Elementary mathematics and beyond 
Please post your image as an attachment.

March 17th, 2017, 02:36 AM  #7 
Newbie Joined: Mar 2017 From: Earth Posts: 5 Thanks: 0 
Ok

August 7th, 2017, 10:21 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 17,919 Thanks: 1384 
Do you still need help with this?

August 8th, 2017, 03:51 AM  #9 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,649 Thanks: 680 
I would do this by "slicing". Assuming the that the cross sections parallel to the xyplane are $\displaystyle \frac{x^2}{a^2}+ \frac{y^2}{4a^2}a= 1$ with $\displaystyle 2a= ce^{\mu z}$ then the area of each ellipse is $\displaystyle (2a)(a)= 4a^2= c^2e^{2\mu z}$. Taking the thickness of each "slice" to be "dz", the volume is given by $\displaystyle \int_{ce^{a\mu}}^{ce^{2a\mu}} c^2w^{2\mu z}dz$.

August 8th, 2017, 12:42 PM  #10 
Global Moderator Joined: Dec 2006 Posts: 17,919 Thanks: 1384 
The area formula for an ellipse should include $\pi$ and $(2a)(a)$ isn't $4a^2$.


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integral calculus, shape, volume 
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