Step 1: Understand the concept of cellular respiration. Cellular respiration is a metabolic process where glucose ($\mathrm{C_6H_{12}O_6}$) is broken down in the presence of oxygen ($\mathrm{O_2}$) to produce carbon dioxide ($\mathrm{CO_2}$), water ($\mathrm{H_2O}$), and energy in the form of ATP.
Step 2: Recall the general balanced chemical equation for cellular respiration. The equation is: $\mathrm{C_6H_{12}O_6} + 6\ \mathrm{O_2} \rightarrow 6\ \mathrm{CO_2} + 6\ \mathrm{H_2O} + \text{energy}$. This equation represents the complete oxidation of glucose.
Step 3: Compare the given options to the balanced equation for cellular respiration. The correct equation should include glucose ($\mathrm{C_6H_{12}O_6}$), oxygen ($\mathrm{O_2}$), carbon dioxide ($\mathrm{CO_2}$), water ($\mathrm{H_2O}$), and energy.
Step 4: Eliminate incorrect options. For example, $\mathrm{C_6H_{12}O_6} + \mathrm{O_2} \rightarrow \mathrm{CO_2} + \mathrm{H_2O}$ is not balanced because it does not account for the correct stoichiometric coefficients. Similarly, $6\ \mathrm{CO_2} + 6\ \mathrm{H_2O} \rightarrow \mathrm{C_6H_{12}O_6} + 6\ \mathrm{O_2}$ represents photosynthesis, not cellular respiration.
Step 5: Identify the correct balanced equation for cellular respiration. The correct answer is: $\mathrm{C_6H_{12}O_6} + 6\ \mathrm{O_2} \rightarrow 6\ \mathrm{CO_2} + 6\ \mathrm{H_2O} + \text{energy}$. This equation satisfies the law of conservation of mass and represents the process of cellular respiration.