March 15th, 2017, 11:24 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 11:22 PM. 
March 16th, 2017, 11:26 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,148 Thanks: 1418 
Do you know how to find a volume of revolution?

March 17th, 2017, 12:14 AM  #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, 02:34 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,148 Thanks: 1418 
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, 02:51 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 11:17 PM. 
March 17th, 2017, 03:08 AM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,641 Thanks: 959 Math Focus: Elementary mathematics and beyond 
Please post your image as an attachment.

March 17th, 2017, 03:36 AM  #7 
Newbie Joined: Mar 2017 From: Earth Posts: 5 Thanks: 0 
Ok

August 7th, 2017, 11:21 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 18,148 Thanks: 1418 
Do you still need help with this?

August 8th, 2017, 04:51 AM  #9 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,822 Thanks: 750 
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, 01:42 PM  #10 
Global Moderator Joined: Dec 2006 Posts: 18,148 Thanks: 1418 
The area formula for an ellipse should include $\pi$ and $(2a)(a)$ isn't $4a^2$.


Tags 
integral calculus, shape, volume 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Shape Volume Calculations  MathsDummy  Math  5  January 24th, 2016 02:45 PM 
Finding Volume of a shape  power11110  Calculus  3  July 22nd, 2013 04:19 AM 
Calculate Volume of a weird cylinder shape.  yunie_  Calculus  1  November 14th, 2011 12:37 PM 
What shape is this?  computronium  Real Analysis  4  June 27th, 2009 07:39 AM 