The layer of the Earth that takes up the most volume is the mantle.

Here's why:

* Mantle: This layer sits beneath the crust and makes up about 84% of Earth's total volume. It's primarily composed of silicate minerals and is incredibly hot, with temperatures reaching over 4,000°C.

* Crust: While the crust is the outermost layer, it's relatively thin compared to the mantle, making up only about 1% of Earth's volume.

* Core: The core, while dense, is much smaller than the mantle, accounting for about 15% of Earth's volume.

So, while the core is the densest part of the Earth, the mantle wins the volume contest by a landslide!