Final answer:
To calculate the cost of filling the pond, we determine the volume of the cylinder filled to three-quarters depth and then multiply by the cost per cubic foot of water. The calculated cost does not match any of the given answer choices.
Step-by-step explanation:
To calculate the cost of filling the cylindrical pond three-quarters of the way with water, we first need to find the volume of water needed. The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. Since the pond has a diameter of 24 feet, the radius is half of that, which is 12 feet. We are given the depth of the pond as 6 feet, but we are only filling it to three-quarters of the depth, which means the height of water will be 4.5 feet (0.75 × 6 feet).
Plugging in the numbers, the volume V = π × (12 feet)^2 × 4.5 feet = π × 144 × 4.5 cubic feet. Using about 3.14 for π, V ≈ 3.14 × 144 × 4.5 ≈ 2050.96 cubic feet. The cost per cubic foot of water is $2.50, so the total cost C to fill the pond three-quarters of the way is C = 2050.96 cubic feet × $2.50/cubic foot ≈ $5127.40.
None of the provided answer choices match this calculation, so it's likely there has been an error in the options given or in our calculation. However, using these numbers and the method described, the answer we find does not correspond to one of the provided choices.