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March 15th, 2017, 11:24 PM   #1
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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.

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Last edited by skipjack; March 16th, 2017 at 11:22 PM.
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March 16th, 2017, 11:26 PM   #2
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Do you know how to find a volume of revolution?
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March 17th, 2017, 12:14 AM   #3
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@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....
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March 17th, 2017, 02:34 AM   #4
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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 $a$.
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March 17th, 2017, 02:51 AM   #5
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@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:



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Last edited by skipjack; August 7th, 2017 at 11:17 PM.
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March 17th, 2017, 03:08 AM   #6
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Please post your image as an attachment.
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March 17th, 2017, 03:36 AM   #7
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Ok
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File Type: jpg NewSketsh.jpg (23.5 KB, 2 views)
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August 7th, 2017, 11:21 PM   #8
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Do you still need help with this?
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August 8th, 2017, 04:51 AM   #9
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I would do this by "slicing". Assuming the that the cross sections parallel to the xy-plane 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 $\displaystyle \int_{ce^{a\mu}}^{ce^{2a\mu}} c^2w^{2\mu z}dz$.
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August 8th, 2017, 01:42 PM   #10
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The area formula for an ellipse should include $\pi$ and $(2a)(a)$ isn't $4a^2$.
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