If you currently have a donut emergency type tire the issue is gonna be width not diameter.

 

It doesn’t come with a donut spare, just repair kit.
I plan to put it in the general trunk space and not underneath where the foam/repair kit is located.

 

Does anyone know if a full size tire 225/40/18 or any tire that is 25 inch in diameter will fit inside the trunk of the Corolla hatchback lying down?

The best way to know is to remove a tire and see if it fits.

 

The tire you mentioned is almost 9" in width. I.E, height when laid flat.
Maybe find a steelie and go with the emergency tire size.

 

Yes it will fit if your just laying it on top. Had a flat last week and was able to put the 18 inch xse wheel in the trunk. I don't have the tire repair kit option so I have a donut (btw, the donut is trash and I cant fit another 18 inch in the donut hole area to swap out the donut). The tire laid in there fine, hatch closed no issue. Doesn't move around either.

 

Irrelevant sedan fact:

I can fit 3 x oem rims with tires on them in the back of my sedan - really surprised at the room in the trunk.

 

Irrelevant sedan fact:

I can fit 3 x oem rims with tires on them in the back of my sedan - really surprised at the room in the trunk.

Try to remove your spare tire and tools. Probably you can fit all 4 wheels.
I did same for my 16" tires (tires only without rims)