I'd like to know what is the word to describe the entire interior within a circle. Circle is for the boundary only and does not include the interior of it.
Mathematically speaking, it's a closed disk.
In geometry, a disk (also spelled disc) is the region in a plane bounded by a circle. A disk is said to be closed if it contains the circle that constitutes its boundary, and open if it does not.
Non-mathematicians will be satisfied to call it just a disk.
Euclidean geometry deals with figures such as: circles, rectangles, etc. The parts inside the figures are simply an area or space. It refers to the space inside the line or lines. Beyond that, there are all sorts of complexities I am not really trained for. :)
"Any time you need to determine the space inside a circle or the amount of space a circle covers, you can use the equation for the area of a circle. Especially for real world applications of this skill, measuring diameter is often the simplest way to start."