Find the Largest 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 that could be enclosed by the stated material is a sphere. The area of a sphere is 4 times pi times the radius squared.Dividing 200 by 4, we get 50 square feet. Dividing 50 by pi, we get 15.916. Taking the square root of that, we get 3.989 feet. So a sphere with a radius of 3.989 feet will enclose the maximum volume.