Setting shapefile points size to actual acerage using QGIS?

Question

I have a shapefile that has lat/long points data of specific facilities in the US. This data is joined with census blocks group population data because eventually I want to calculate how many people live within a 1 mile and 3 mile radius of each facility.

The issue I am having is I do not want just a uniform point for each facility. I want each point to be represented by how many acres the facility is (I have acreage data in the table).

Now in QGIS, I can arrange the size of each point based on acreage, but its not geographically accurate. It just shows that small acre plots are 1 pixel in width, and big acre lots are >1 pixel in width. (I did this by using the "Assistant | Symbol Size" tool in the "Symbols" tab of "Layer Properties"

How can I get each point to physically be the acre size, and then create the 1 and 3 mile buffers around that? So if there is a plot of land that is 25 acres, I want a circle that is exactly 25 acres in size. THEN place a 1 mile and 3 mile boundary on that.

Some photos to help explain what is going on.

Here, the points are all uniform (with the 1 mile boundary in purple, 3 mile boundary in blue), but I would like them to be based on the actual acreage. Like if the plot of land was 25 acres, I want a circle that is exactly 25 acres in size.

I can adjust the points like this, but its not physically and geographically real to the size of the acre. Now I understand that maybe the boundary of these plots of land are not uniformly circular, but that is an assumption I am making to make the analysis possible.

My methodology. need help with step 2

I am using QGIS.

EDIT

Answer 1

You could use the Variable Distance Buffer tool, and reverse-compute the radius to be used for such buffers using the acres.

1. Add a new attribute to your table for the radiuses : R = sqrt(A / pi)
2. Run the Variable Distance Buffer tool, with the radiuses as input. You should perhaps use a big enough number of segments to have shapes that are close enough to circles.
3. Run the regular Buffer tool twice more to generate those 1 and 3 miles buffer.

Although, be careful with your units, and first make sure that your points aren't in a geodetic system like WGS84. If I understand correctly, they currently are just lat/long objects ? You might want to convert them first, and work with a local CRS (otherwise your parameters might be interpreted as degrees, and nobody wants a buffer that's some degrees wide in radius...)