Final answer:
After substituting r = 4 and h = 5 into the given formula for S and performing the calculations, S is found to be approximately 226.1 when rounded to the nearest tenth. None of the provided options exactly match this calculated value.
Step-by-step explanation:
If S = 2(3.14r^2 + 3.14rh), we need to determine the value of S when r = 4 and h = 5. Substituting these values into the formula, we get:
S = 2(3.14 × 4^2 + 3.14 × 4 × 5)
S = 2(3.14 × 16 + 3.14 × 20)
S = 2(50.24 + 62.80)
S = 2(113.04)
S = 226.08
When rounded to the nearest tenth, S is approximately 226.1. Therefore, the closest option to our calculated value is Option C: 251.2, but we must acknowledge that none of the provided options exactly match the calculated value of S.