On the relationship between volume and surface area

Krenicky, Joseph; Rychtář, Jan

doi:10.2140/involve.2010.3.1

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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

DOI: 10.2140/involve.2010.3.1

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

Vol. 3, No. 1, 2010