Jun 5, 2010 · The discussion focuses on maximizing the volume of a rectangular box inscribed within the ellipsoid defined by the equation (x^2/a^2) + (y^2/b^2) + (z^2/c^2) = 1. The volume of the box is …

Jun 2, 2013 · The problem involves finding the volume of the largest rectangular box in the first octant, constrained by the plane equation x + 2y + 3z = 6. The original poster expresses difficulty in …

Nov 6, 2008 · The discussion focuses on maximizing the volume of a rectangular box inscribed in a sphere of radius 1. The volume is expressed as V = xyz, with the constraint x² + y² + z² = 1. …

Nov 19, 2003 · The discussion focuses on maximizing the volume of a rectangular box inscribed within the ellipsoid defined by the equation 9x² + 36y² + 4z² = 36. The correct approach involves using the …

Dec 9, 2012 · The problem involves determining the rate of change of the volume of a rectangular box given specific dimensions and rates of change for length, width, and height.

Sep 29, 2011 · The cereal box is a rectangular prism with a volume of 2500 cm³. The dimensions are defined by the relationships: the width (w) is four times the depth (d), and the height (l) is five …

Dec 26, 2009 · The problem involves maximizing the volume of a rectangular box given constraints on the amount of wire and paper available for its construction. The subject area includes geometry and …

Mar 2, 2009 · The problem involves optimizing the dimensions of a rectangular box with no top, given a fixed volume of 256 cubic inches. Participants are tasked with minimizing the amount of cardboard …

Oct 25, 2005 · The problem involves finding the greatest possible volume of a rectangular box inscribed in an ellipsoid defined by the equation 96x^2 + 4y^2 + 4z^2 = 36. The original poster is exploring the …

Aug 27, 2008 · The discussion revolves around finding the dimensions of a rectangular box that maximizes volume while adhering to a surface area constraint of 64 cm². The problem involves …