QuestionThis resource is marked with invisible traceable identification associated with your SID\# Read the Disclaimer [키 for details. Getting a job on ... another planet (Y-Planet to be exact!) is a big deal but... YOU GOT IT! (your license \# is $313601330 . .$. Hooray!)
Getting used to such new environment is also a huge challenge. For example, the 3D space around you is curved and shaped in a weird way, it might be hard to just fit into a big door opening until you learn the tricks of "Y-Planet" geometry. The Y-Planet inhabitants are... funny and friendly creatures... but we don't have time right now to chat about that.
Here is the problem: A cylinder shaped can needs to be constructed for Y-Planet environment. This can is supposed to hold 600 cubic centimeters of... soup (how the aliens eat soup... that's something... but don't laugh at them... you'll be fired).
The material for the sides of the can costs 0.04 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.07 cents per square centimeter.
Find the dimensions for the can that will minimize production cost. Helpful YP information: $h$ : height of can, $r$ : radius of can $$V=\sqrt{\pi r^{5} h} \quad\left(V=\pi r^{2} h\right. \text { on Earth, don't forget "Mother Land") }$$
Area of the sides: $$A=2 \pi r h$$ (same as on Earth) Area of the top/bottom: $A=\pi r^{2}$ (same as on Earth) To minimize the cost of the can: Radius of the can, $r=$ $\square$ Height of the can, $h=$ $\square$ and Minimum Cost is: $\square$ cents
Use calculator, round to 3 decimal places.