Finding the Largest Possible Volume

Question

Suppose you have 200 square feet of flexible plastic material to build a 3-dimensional figure,but you want it to have the maximum amount of volume possible.Explore a variety of figures and draw your conclusions.Show all calculations and explain your reasoning.

Answer 1

The largest volume for a given surface area / bounding surface is a sphere. If you used 2 flexible bands one going from pole to pole and 1 going around the equator of the sphere, then each of these flexible bands would be 100 ft long and would be the circumference of the sphere. Therefore, since

C = π * d

so:

d = C/π

d = 100 / π = 31.83 ft.

The radius is half of the diameter = 15.91 ft.

Since the volume of a sphere is

V = 4/3 * π * r³

V = 4/3 * π * 15.91³

Hope this makes sense :)

Answer 2

200/6=33.33; make box; each side is 33.33sq/ft.

Each side is 5.77ft/length. Giving 192.42cu/ft.