Step 1: Understand the concept of cellular respiration. Cellular respiration is the process by which cells convert glucose ($\mathrm{C_6H_{12}O_6}$) and oxygen ($\mathrm{O_2}$) into carbon dioxide ($\mathrm{CO_2}$), water ($\mathrm{H_2O}$), and energy (in the form of ATP). This is a key metabolic pathway in living organisms.
Step 2: Recall the general formula for cellular respiration. The balanced chemical equation for cellular respiration 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: Analyze the options provided. Compare each option to the general formula for cellular respiration. The correct equation should include glucose ($\mathrm{C_6H_{12}O_6}$) and oxygen ($\mathrm{O_2}$) as reactants, and carbon dioxide ($\mathrm{CO_2}$), water ($\mathrm{H_2O}$), and energy as products.
Step 4: Eliminate incorrect options. For example, the first option represents fermentation, not cellular respiration. The second option represents photosynthesis, which is the reverse of cellular respiration. The third option is incorrect because it does not balance the reactants and products properly.
Step 5: Identify the correct equation. The correct balanced chemical equation for cellular respiration is: $\mathrm{C_6H_{12}O_6} + 6\ \mathrm{O_2} \rightarrow 6\ \mathrm{CO_2} + 6\ \mathrm{H_2O} + \text{energy}$. This matches the process of glucose oxidation in the presence of oxygen.