Area of a circle: why is it πr^2 and not πd^2? Need a quick way to remember

I keep tripping over the area of a circle because I always grab the diameter instead of the radius. Everyone says A = πr^2, but my brain sees a diameter and wants to square that. For example, if the diameter is 10 cm, my first instinct is π·10^2 = 100π. Then I remember it’s the radius, so maybe it should be π·5^2 = 25π. I think 25π is the right one, but I keep second-guessing myself.

Can someone explain, in plain terms, why it has to be the radius that gets squared and not the diameter? Also, what’s the fastest mental path from a given diameter to the area without writing much down? Any dead-simple trick to sanity-check 100π vs 25π so I don’t pick the wrong one?

Bonus: if I double the diameter (say from 10 to 20), should the area really go up by four times, and is there a quick way to see that without a big proof? A couple of small, practical checks would help lock this in.