$1)$ Plate

Constraints:

$-$You are to use Cartesian functions $(\backslash ($ x$,$ y $\backslash ))$ to design a ceramic dinner plate.

$-$You will set this up with functions such that rotating them about the $\backslash ($ y $\backslash )-$axis creates the dinner plate.

$-$The plate needs to have:

$-$ a largest diameter between $10$ and $12$ inches;

$-$ a max height between $1$ and $2$ inches;

$-$ a steady base; and

$-$a more$-$or$-$less flat well so food doesn't get stuck or slide off.

Calculations

$-$Square footage of food that it can hold; and

$-$The total amount of ceramic needed to craft it$.$

Below you can see the outline of a small saucer made of $3$ functions: $1$ for the base, a second for the rim, and a third for the indentation that a teacup would sit in$.$ Note that these equations have restricted input bounds so as to not continue forever