The area of a circle with a diameter of 30 feet is approximately 706.858 square feet.
To find the area of a circle, you can use the formula:
$ A = \pi r^2 $
where $ A $ is the area, $ \pi $ is a constant (approximately 3.14159), and $ r $ is the radius of the circle.
Find the Radius: The radius is half of the diameter. Since the diameter is 30 feet, the radius $ r $ is $ \frac{30}{2} = 15 $ feet.
Apply the Area Formula: Use the area formula with the radius found in step 1.
$ A = \pi r^2 $
$ A = \pi (15)^2 $
$ A = \pi (225) $
$ A \approx 3.14159 \times 225 $
$ A \approx 706.858 \text{ square feet} $
To ensure the answer is correct, you can re-calculate the area using the same steps or check with a calculator that can handle π to confirm the result.
Pi (π): Pi is a mathematical constant representing the ratio of a circle's circumference to its diameter. It is approximately 3.14159 but can be represented as $ \pi $ in calculations for more precision.
Radius: The radius of a circle is the distance from the center of the circle to any point on its circumference. It is half the length of the diameter.
Area of a Circle: The area of a circle is the number of square units inside the circle. The formula $ A = \pi r^2 $ allows you to calculate the area if you know the radius.
Units: When calculating area, the result will be in square units. In this case, since we are working with feet, the area will be in square feet.
Precision: The value of π used in calculations can affect the precision of the area. For more accurate results, use more digits of π or use a calculator with a π function.
By following these steps and understanding the related concepts, you can accurately determine the area of a circle for any given diameter.