Here's why:

* Mantle Size: The mantle makes up about 84% of the Earth's total volume, making it the largest layer.

* Composition: It is primarily composed of silicate minerals like olivine and pyroxene.

* Core vs. Crust: The Earth's core, while containing a large mass, is relatively smaller in volume compared to the mantle. The crust, the outermost layer, is extremely thin in comparison.

Therefore, the Earth's greatest bulk composition, based on volume, is found in its mantle.