So we’re going from a 6” pizza to a 24” pizza

The 6” has a radius of 3”
To find area we multiply pi * r² to get 28 square inches
For the 24”, pi * 12², or 452 square inches

The 24in has 4x the diameter but is 16x the area, this is where you’re getting the 13x number.
The math works about the same for the moon and earth
3.7x diameter, 13x area sounds right

But we’re not calculating area, only comparing their size ratios.

Since the Earth is 4x the size of the moon, and we’re the same distance, the earth would look 4x bigger from the moon as the moon does from Earth

The “blue marble” photo looks huge!
taken 18k miles from earth, so why doesn’t Earth look huge from the moon? Because the moon is 240k miles away, on the surface of the moon that photo would appear 13x smaller


Does that all make sense?