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Topic: Volume and surface area of a sphere
Replies: 0

 William J. Larson Posts: 117 Registered: 12/3/04
Volume and surface area of a sphere
Posted: May 4, 1998 11:34 AM

=3D=3D>When one gets the derivative of the volume of a sphere with respec=
t
=3D=3D>to its radius, one gets the surface area. Obviously, this is not
=3D=3D>the case with cubes. Does anybody know why this is true with
=3D=3D>spheres?

But it IS the case with cubes. =

Write V =3D (2r)^3, where r is the perpendicular distance from =

the origin to a face. =

dV/dr =3D 24r^2 which is the surface area.

You need to express the volume in terms of one parameter
"r" where r must (I think) be perpendicular to the surface.
This is so that you could have gotten the volume by =

integrating S(r) dr.

You just have to choose the right coordinates. =

I suspect that the sphere & the cube are the only solids
with enough symmetry to play this trick, but maybe it =

can be done with any of the regular solids. =

William J. Larson
Switzerland
phone/fax: (41 22) 362 7984
email: Bill_Larson@compuserve.com