maximizing+volume+and+minimizing+surface+area

EXAMPLE:
EXAMPLE:

A company is trying to choose between 2 boxes with the dimensions below. Which design has the greater surface area thus requirs more material for the same volume
A company is trying to choose between 2 boxes with the dimensions below. Which design has the greater surface area thus requirs more material for the same volumehttp://anthro.palomar.edu/adapt/adapt_2.htmhttp://anthro.palomar.edu/adapt/adapt_2.htmhttp://anthro.palomar.edu/adapt/adapt_2.htm

the boxes above have a volume of 64 cubic inches.
the boxes above have a volume of 64 cubic inches.

the surface area of the square is 6(4)^2 = 96 cubic inches.
the surface area of the square is 6(4)^2 = 96 cubic inches.

The surfacea area of the rectangular prism is 2(2)(4) + 2(4)(8) + 2(2)(8) = 112 cubic inches.
The surfacea area of the rectangular prism is 2(2)(4) + 2(4)(8) + 2(2)(8) = 112 cubic inches.

the rectangular prism has the greater surface area.
the rectangular prism has the greater surface area. = =

= = =12 by 10 inch open box= In the column side of square ,x. You are cutting inches into the box. length and width get smaller then by how many times you cut in


 * ===Side of Square, x=== || ===Length, l=== || ===Width, w=== || ===Height, h=== || ===Volume, lwh=== ||
 * 1 || 10 || 8 || 1 || 80 in^3 ||
 * 2 || 8 || 6 || 2 || 96 in^3 ||
 * 3 || 6 || 4 || 3 || 72 in^3 ||
 * x || x-2 || x-2 || x || lwh ||

=5 by 8 foot open box=


 * ===Side of Square, x=== || Length, l || Width, w || Height, h || Volume, lwh ||
 * 1 || ? || ? || ? || ? ||
 * 1.5 || ? || ? || ? || ? ||
 * 2 || ? || ? || ? || ? ||

Answers to 5 by 8 foot open box