Calculate the area of a circle with a circumference of 69.08 meters.

Calculate the area of a circle with a circumference of 69.08 meters.

What does "Calculate the area of a circle with a circumference of 69.08 meters" mean? Understand first

To calculate the area of a circle with a given circumference of 69.08 meters, we need to find the amount of space enclosed within the circle. The area of a circle is the measure of the surface inside the circle, and it is expressed in square units.

What is the answer to "Calculate the area of a circle with a circumference of 69.08 meters"? Give the answer first

The answer to calculating the area of a circle with a circumference of 69.08 meters is approximately 371.94 square meters.

How to solve the problem: hints

Method 1: If radius is given

1. First, list the formulas for calculating the area and radius of a circle.

   • Area of a circle: A = πr^2
   • Radius of a circle: r = C / (2π), where C is the circumference of the circle.

2. Plug the radius of the circle into the formula for the area.

   • A = π * (C / (2π))^2

3. Finally, calculate the area using the given circumference and express the answer in numbers.

Method 2: If diameter is given

1. First, list the formulas for calculating the area and diameter of a circle.

   • Area of a circle: A = πr^2
   • Diameter of a circle: d = C / π, where C is the circumference of the circle.

2. Plug the diameter of the circle into the formula for the area.

   • A = π * (d/2)^2

3. Calculate step by step using the given circumference and express the answer in numbers.

Method 3: If the circumference of the circle is given

1. First, list the formulas for calculating the area and circumference of a circle.

   • Area of a circle: A = πr^2
   • Circumference of a circle: C = 2πr, where r is the radius of the circle.

2. Plug the circumference of the circle into the formula for the area.

   • A = π * (C / (2π))^2

3. Finally, calculate the area using the given circumference and express the answer in numbers.

Step by step solution to calculate the area of a circle with a circumference of 69.08 meters and finally get the answer, expressed in numbers

1. Calculate the radius of the circle using the formula: r = C / (2π)

   • r = 69.08 / (2π)
   • r ≈ 11.00 meters

2. Plug the radius into the formula for the area of a circle: A = πr^2

   • A = π * (11.00)^2
   • A ≈ 379.94 square meters

3. Round the answer to the appropriate number of significant figures: A ≈ 371.94 square meters

Therefore, the area of a circle with a circumference of 69.08 meters is approximately 371.94 square meters.

What is a circle?

A circle is a two-dimensional geometric shape that consists of all points in a plane that are equidistant from a fixed center point. It is perfectly round and has no corners or edges.

How to draw a circle?

To draw a circle, you can use a compass, which is a tool with two arms. One arm has a sharp point, and the other arm has a pencil or pen attached to it. Place the sharp point at the center of the circle and rotate the compass around it, keeping the pencil or pen in contact with the paper. This will create a perfect circle.

What data does the circle have?

A circle has several important measurements:

• Radius: The distance from the center of the circle to any point on its circumference.
• Diameter: The distance across the circle, passing through the center and touching two points on the circumference. It is equal to twice the radius.
• Circumference: The distance around the circle.
• Area: The measure of the surface enclosed within the circle.

What does Π mean?

The symbol Π (pi) represents the mathematical constant that is the ratio of the circumference of any circle to its diameter. It is an irrational number, approximately equal to 3.14159, but it can be rounded to 3.14 for most calculations.

The origin of Π?

The origin of the symbol Π (pi) can be traced back to ancient Greece. The Greek mathematician Archimedes was the first to use the symbol to represent the ratio of the circumference of a circle to its diameter. The symbol Π comes from the Greek word "perimetros," meaning circumference.

Frequently asked questions about circles

Question: Calculate the area of a circle with a circumference of 69.08 meters.

To calculate the area of a circle with a given circumference of 69.08 meters, you can use one of the methods mentioned above. By plugging the circumference into the appropriate formula, you can find the radius and then calculate the area using the formula A = πr^2. The answer to this specific question is approximately 371.94 square meters.