Final answer:
The area of the base of the cylindrical vat used to make grape juice with a diameter of 16 feet is approximately 200.96 square feet.
Step-by-step explanation:
To find the area of the base of the cylindrical vat used to make grape juice, we need to find the area of a circle. The formula for the area of a circle is A = πr², where r is the radius of the circle. In this case, we are given the diameter, which is 16 feet, so we can find the radius by dividing the diameter by 2. Therefore, the radius is 8 feet.
Now, substituting the radius into the formula, we get A = 3.14 x (8 feet)² = 3.14 x 64 = 200.96 square feet.
Rounding to the nearest hundredth, the area of the base of the cylindrical vat is approximately 200.96 square feet.