Re: Calculation of the surface after intersection of two spheres
- To: mathgroup at smc.vnet.net
- Subject: [mg100905] Re: Calculation of the surface after intersection of two spheres
- From: dh <dh at metrohm.com>
- Date: Thu, 18 Jun 2009 04:50:44 -0400 (EDT)
- References: <h19i7g$p78$1@smc.vnet.net>
Hi Horacius,
place the spheres symmetrical on the x axis at -0.5 and 0.5. Then the
intersection is at x=0. The total surface is twice that of one sphere.
Now, consider the truncated sphere as a rotation surface. The radius:
y[x] as a function of x. Use the formula for the surface of a rotation
body. Then integrate for x=0 to x=1.1. This is implemented her:
===========================================
r = 0.6;
x0 = 0.5;
y[x_] = Sqrt[r^2 - (x - x0)^2];
Plot[ {y[x, 0.5]}, {x, 0, 1.1}, AspectRatio -> Automatic]
2 Integrate[2 y[x] Pi Sqrt[1 + y'[x]^2], {x, 0, 1.1}]
==========================================
Daniel
Horacius ReX wrote:
> Hi,
>
> I have two spheres of radius 0.6 whose origins are separated a
> distance of 1. So the spheres overlap and I want to calculate the
> total surface now.
>
> For that purpose I started to calculate the surface of the separated
> spheres, which is trivial and I can do by hand, but after they
> intersect or overlap, how can I tell the program to calculate the
> surface ?
>
> Thanks in advance
>