Methane consists of a central carbon atom bonded to four hydrogen atoms. The carbon atom undergoes \( sp^3 \) hybridization, where its one \( 2s \) orbital and three \( 2p \) orbitals mix to form four equivalent \( sp^3 \) hybrid orbitals. These hybrid orbitals are directed towards the corners of a regular tetrahedron, with bond angles of approximately \( 109.5^\circ \).
The tetrahedral arrangement minimizes electron pair repulsion, as predicted by VSEPR (Valence Shell Electron Pair Repulsion) theory. This results in a symmetrical tetrahedral shape for the methane molecule.
Final Answer: The shape of the methane molecule is \( \mathbf{\text{tetrahedral}} \), which corresponds to option \( \mathbf{(3)} \).