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Thread Subject:
Calculating volume

Subject: Calculating volume

From: Johan VAN RENSBURG

Date: 9 Oct, 2010 03:19:04

Message: 1 of 3

Hi guys
Can anybody tell me how to calculate the volume of:
0.25Z^2 = 0.09X^2 + 0.16Y^2
Thanks in advance
Jvr

Subject: Calculating volume

From: Image Analyst

Date: 9 Oct, 2010 04:13:04

Message: 2 of 3

Jvr:
Well, over all possible x and y, and going from the z=0 plane up to the surface, wouldn't that be infinity?

Subject: Calculating volume

From: Roger Stafford

Date: 9 Oct, 2010 05:05:30

Message: 3 of 3

"Johan VAN RENSBURG" <johan.jansevanrensburg@live.vu.edu.au> wrote in message <i8omv8$ns8$1@fred.mathworks.com>...
> Hi guys
> Can anybody tell me how to calculate the volume of:
> 0.25Z^2 = 0.09X^2 + 0.16Y^2
> Thanks in advance
> Jvr
- - - - - - - - - - - -
  That is the surface of a double ellipsoidal cone with vertex at the origin. The surface has no volume, but if you want the volume inside it from z = 0 to z = h, it would be 25/36*pi*h^3.

  That is because the volume of such a cone is one-third its height times the area of its base. The height is h. The base is the ellipse

 0.25*h^2 = 0.09*x^2 + 0.16*y^2

 or

 x^2/(.25*h^2/.09) + y^2/(.25/h^2/.16) = x^2/a^2 + y^2/b^2

where a = 5/3*h and b = 5/4*h. Its area is pi*a*b = pi*25/12*h^2. Hence the volume is (1/3*h)*(pi*25/12*h^2) = 25/36*pi*h^3.

Roger Stafford

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