As the others are pointing out, the cow needs space to walk, lay, dig, play in mud, etc. She will use about 1/2 acre for that - the 'drylot'.
Something like 1/2 acre to 1 acre of real pasture should keep your cow pretty happy on grass. From fall to late spring you will need to feed hay - close to a bale a day.
If you want her to grow a calf & provide milk, she will need more. Either you have to add grains every day, or something high in protien - good alfalfa, or another acre or so to graze. She needs energy to give milk plus be growing another calf inside here.
There are dry times when grass stops growing, and what is left is dry stems in the pasture. _Real_ good for the bulk she needs, but hardly any enegry left in it. Other times, your pasture will grow too fast for her to keep up with it.
As well, what will you do with the calf? Will it be around for some time, also stomping, digging up, etc. a drylot, and needing a little bit of grass as it ages.
A cow or horse will like tender new grass. They will let some grass grow old & stemmy, and keep eating the tender stuff over & over until it dies more or less.
In this way, if you have cattle on a spot too small for them, they will end up killing off the good grass, & promoting the poorer stuff to grow.
If you would have 3 different areas of 1/2 acre each, then you can place the cow in one, let her clean it up, place her in the next one, and so on. Each plot will have 2-3 weeks to regrow & become strong again. As well any worms or etc. tend to die out with the rest between grazings.
This type of rotation is just a win win win for everyone. You get much more good grass, the cow is healthier & happier, you don't need to buy as much feed.....
A 1/2 acre pasture would do pretty good for a cow, tho you would need to add some purchased feed most all of the year. If you have a lot for her to rest & poop & mud in the 1/2 acre will go a long ways.....
A 1/2 acre drylot if this is all she has won't feed her very much at all as the grass slowly disappears & fills in with mud & weeds....
--->Paul