Vol. 3, No. 1, 2010

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On the relationship between volume and surface area

Joseph N. Krenicky and Jan Rychtář

Vol. 3 (2010), No. 1, 1–8
Abstract

We show that the statement that the surface area is the derivative of the volume, which is well known for a ball, can be generalized and stated in a proper way for any set with finite volume and surface area. We also provide a specific statement for star-shaped sets.

Keywords
volume, surface, star-shaped sets
Mathematical Subject Classification 2000
Primary: 28A75, 51M25
Milestones
Received: 30 December 2008
Accepted: 7 January 2010
Published: 20 April 2010

Communicated by Kenneth S. Berenhaut
Authors
Joseph N. Krenicky
Department of Physics
The University of North Carolina at Greensboro
Greensboro, NC 27403
United States
Jan Rychtář
Department of Mathematics and Statistics
The University of North Carolina at Greensboro
Greensboro, NC 27403
United States