No, the core is not the most expansive layer of the Earth.

Here's why:

* The mantle is the largest layer. It makes up about 84% of the Earth's volume, while the core only accounts for about 16%.

* The crust is the thinnest layer. It's only about 3 to 45 miles thick, depending on whether it's oceanic or continental crust.

Here's a simplified breakdown of the Earth's layers by size:

1. Mantle: The largest layer, containing the most volume.

2. Core: Second largest, composed of the inner and outer core.

3. Crust: The thinnest layer, encompassing the Earth's surface.