One 18 inch pizza has more 'pizza' than two 12 inch pizzas (twitter.com)

Another way to think about it: It's because 1.5 > √2.

To exactly double the area of a figure, scale any linear dimension up by √2. If you scale by more than that, you'll more than double the area.

For area, the change in size is the square of the old:new ratio.

Two dimensions, so X * X

For volume, the change in size is the cube of the old:new ratio.

Three dimensions, so X * X * X