The country of Erehwon, in an effort to economize has decided to revise its coinage. The treasury has a very large supply of zinc discs whose radius is exactly 1 rog. [Of course this means that each disc has an area of π square rogs.]
The treasury decides that they can increase the number of coins they can make from a given disc by stamping a concentric circular hole in the disc and using the ring for one coin and the stamped out small disc as a second coin.
This environment shows a plot of the area of the ring coin and the smaller disc coin plotted as a function of the radius of the cutout.
• Write an algebraic expression for each of these graphs.
• If the government decides to value the ring coin as one Erehwon rial [1 ϖ] and the smaller disc coin as one half rial [ ½ ϖ ] what should the dimensions of each be? Can you offer an alternative suggestion? Which suggestion do you prefer and why?
• What do you think the length of the green line tells you? Why do you think so?
• The country is very impressed with the US coinage system and would also like to have additional coins that have the following fractional values – ¼ rial, 1/10 rial, 1/20 rial
Can you suggest an efficient strategy for doing this?