A hands$-$on technology museum has hired you to do background research on the feasibility of a new activity to allow visitors to assemble their own ferrite core memory device$$a technology in common use until the $1970$s$,$ and in specialized applications after that. The computers onboard the early space shuttle flights used core memory due to their durability, nonvolatility, and resistance to radiation$$core memory recovered from the wreck of the Challenger still functioned.

Ferrite core memory comprises numerous tiny ferrite rings $($cores$)$ in a grid, each of which has either two or three wires threaded through it in a repeating pattern and can store a single bit, or binary digit$$a $0$ or a $1.$ Since the cores were typically on the order of one millimeter in diameter, workers had to assemble these under microscopes.

After investigating ferrite materials, you find several that would be suitable for fabrication of the cores. The museum staff has decided to have the visitors assemble a array $(16$ cores$$actual devices were MUCH larger$)$ and anticipate that $2500$ people will assemble one of these over the course of the project. Assuming that the cores are each cylindrical rings with a hole diameter half that of the outside diameter of the ring and a thickness one$-$fourth the outside diameter, you need to know how many grams of ferrite beads you need to purchase with $10\%$ extra beyond the specified amount for various core diameters and ferrite materials. You also wish to know the total cost for the beads.

The user will enter the compound name, the specific gravity, and the cost per gram of the material. Create a table showing the number of pounds of cores for core diameters of $1\mathrm{.}2$ to $0\mathrm{.}7$ millimeter in $0\mathrm{.}1$ millimeter increments as well as the total cost. For cores with a diameter less than $1$ millimeter, there is a $50\%$ manufacturing surcharge, thus the smallest cores cost more per gram. Include table entries for individual core volume and total volume of all cores.