Final answer:
The exact area of a circle with a diameter of 18 feet is approximately 254 square feet, calculated using the formula A = πr² with the radius as half of the diameter.
Step-by-step explanation:
The student is asking for the exact area of a circle with a diameter of 18 feet. To find the area, we use the formula A = πr², where A is the area, π (pi) is approximately 3.14159, and r is the radius of the circle. Knowing that the diameter is 18 feet, we first need to calculate the radius, which is half of the diameter, so in this case, the radius (r) is 9 feet. Plugging this into the formula, we get:
A = π × 9² = 3.1415927... × 81 = 254.4690047 square feet
Now, since we started with a diameter that has a two significant figures, our answer should also be reported with two significant figures for precision. Therefore, the exact area of the circle is approximately 254 square feet.