Final answer:
To calculate the area of a vertical cross-section through the center of the pool, you find the diameter from the circumference and multiply it by the pool's height. The calculated area is 96 square feet, which does not match the options given in the question.
Step-by-step explanation:
To find the area of a vertical cross-section through the center of the cylindrical swimming pool, we need to calculate the area of a rectangle since the cross-section would be a rectangle with the height of the pool as one of its sides and the diameter of the pool as the other side. The circumference of the pool (C) is given as 75.36 feet and the height (h) is 4 feet. Since circumference C = 2πr, where r is the radius of the cylinder, we first find the radius (r).
r = C / (2π) = 75.36 / (2 × 3.14) = 75.36 / 6.28 ≈ 12 feet
The diameter (d) of the cylinder is twice the radius. So, d = 2 × r = 2 × 12 = 24 feet.
Next, we calculate the cross-sectional area (A) which is A = h × d = 4 feet × 24 feet = 96 square feet. Therefore, the area of a vertical cross-section through the center of the pool is 96 square feet. This answer is not listed among the provided options, indicating a possible mistake in the question or the options provided.