Question

PLEASE HELP ASAP!!!! 100% CORRECT ANSWERS ONLY PLEASE!!!! I CANNOT RETAKE THIS

Answer 1

The first statement is true. Reasoning below.

= = =

We want to find the area of a fixed circle, so we can throw out the last option. If
`r` changes at all, then so does the area of the circle.

For
`s` to increase would require using a circumscribed polygon with less sides. Again, the circle is fixed, so only a certain length
`s` can fit inside the circle. This eliminates the third option.

Note that if we use a regular hexagon, then
`s=r` automatically, because the component triangles that make up the hexagon are equilateral. Increasing
`h` would require that we use a polygon with more sides, which would simultaneously make
`s` stray away from
`r`. In other words, if
`h` increases, then
`s` decreases, so we can never eventually have
`s\to r` (
`r` is fixed).

That leaves the first option. Indeed, as
`n` increases, we get a polygon that looks increasingly rounder and more like a perfect circle. At the same time, that means
`h` gets larger, but would be bounded above by the circle's perimeter. So as
`h` increases indefinitely, it will eventually "be equal" (in the limit sense) to
`r`, so that
`rh\to r^2`.