In other words, what container (spherical, cylindrical, conical, etc.) could hold 12 ounces of liquid and have the LEAST surface area? And what are the dimensions (height, radius, side lengths, etc) of this container?
Note: 12 ounces = 354 cm^3 (this is the conversion factor, as it made it a lot easier)
So far, I have a cylinder as the most efficient container.
12 ounces = 354.882 cm^3***
I’m supposed to present this with proof involving calculus (application of derivatives/optimization,etc). And I’ve tried a cylinder and a cone. The cylinder had less between those two.
Thanks for the answers guys.
My calculated MINIMUM surface areas are:
Cylinder: 277.490 cm²
Cone: 305.409 cm²
Sphere: 242.401 cm²
Answer by Big Daddy
Have you checked both cubes and spheres?