Answer :
Final answer:
To find the missing side length in the formula for the volume of a rectangular prism, set up an equation and solve for the variable c.
Explanation:
To find the missing side length in the formula for the volume, we can set up an equation and solve for c. The formula for the volume of a rectangular prism is V = lwh, where l, w, and h represent the lengths of the three sides. In this case, the formula given is V = 223 + 17c^2 + 46c + 40. Comparing this to the volume formula, we can see that the missing side length corresponds to the variable c. We can set up the equation 17c^2 + 46c + 40 = 0 and solve for c using factoring, completing the square, or the quadratic formula. Solving this equation, we find that c = 3. Therefore, the missing side length is c = 3, so the answer is C.
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