Associated Topics || Dr. Math Home || Search Dr. Math

### Volume of an Elliptical Frustum

```
Date: 12/01/1999 at 07:46:49
From: Alan Macleod
Subject: An elliptical frustum

Dear Doc,

Deriving the Volume of a Frustum
http://mathforum.org/dr.math/problems/taylor5.6.98.html

the volume of a frustum is

V = (1/3)*pi*(R^2*H - r^2*(H-h))

and

H = Rh/(R-r)

From other articles:

The volume of a cone is

V = (1/3)*pi*R^2*h

and the volume of an elliptical cone is

V = (1/3)*pi*a*b*h

Can I therefore assume that the volume of a elliptical frustum is:

V = (1/3)*pi*[(a*b)*H - (c*d)*(H-h)]

and

(sqrt(a*b))*h
H = ---------------------
sqrt(a*b) - sqrt(c*d)

where

a = semi-major axis of base
b = semi-minor axis of base
c = semi-major axis of top
d = semi-minor axis of top

If not, then can you give me the correct formulas?
```

```
Date: 12/01/1999 at 10:02:08
From: Doctor Rob
Subject: Re: An elliptical frustum

Thanks for writing to Ask Dr. Math, Alan.

Yes, the volume of an elliptical frustum is

V = (1/3)*pi*[(a*b)*H - (c*d)*(H-h)]

The last part is also correct, but you can avoid the square roots if
you realize that a/c = b/d = H/(H-h). Then you can use instead

H = a*h/(a-c) = b*h/(b-d)

- Doctor Rob, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search