Pyrolusite is an ore of manganese, and its chemical formula is MnO\(_2\). It is a primary source of manganese, which is widely used in the production of steel, batteries, and other industrial applications. The mineral is dark and often found in sedimentary rocks.
Manganese dioxide (MnO\(_2\)) occurs naturally as pyrolusite and is used in the manufacturing of dry cell batteries and in the production of chlorine and potassium permanganate.
Other options like CaSi\(_3\), CuCO\(_3\), and Al\(_2\)O\(_3\) refer to different minerals and are not the correct answer for Pyrolusite ore.
Thus, the correct answer is (B) MnO\(_2\).