Determine the area of a circle with a diameter of 30 feet.

Answer

The area of a circle with a diameter of 30 feet is approximately 706.858 square feet.

Method: Hints

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.

Calculation Steps and Description

1. 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.

2. Apply the Area Formula: Use the area formula with the radius found in step 1.

$A=\pi r^2$

$A=\pi (15{)}^2$

$A=\pi (225)$

$A\approx 3.14159\times 225$

$A\approx 706.858\text{ square feet}$

Verification

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.

Related Knowledge Points and Detailed Explanation

• 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.