Final answer:
The volume of liquid in the cylindrical vat filled to a depth of 18 feet is approximately 1,414 cubic feet, calculated using the formula V = πr²h with a radius of 5 feet.
Step-by-step explanation:
To find the volume of liquid in a cylindrical vat when it is filled to a specific depth, you use the formula for the volume of a cylinder V = πr²h, where V is volume, r is radius, and h is height. Given that the diameter of the vat is 10 feet, its radius is 5 feet. When filled to a depth of 18 feet, the volume of the liquid in the vat can be calculated as V = π × 5² × 18 cubic feet.
To perform the calculation: V = 3.14159 × 25 × 18. So the volume of the liquid is approximately 3.14159 × 450, which is about 1,413.71 cubic feet. Therefore, the vat contains approximately 1,414 cubic feet of liquid (rounded to the nearest cubic foot).