Find 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

For a sphere A=4(pi)r² V=4/3(pi)r³

^{set A=200 solve for r, then plug that value}

^{into the formula for V. That gives maximum}

^{volume for 200 square feet of material}

^{No need to try alternative 3 dimensional figures.}

^{Sphere gives the maximum}