Calculate the area of a circle with a circumference of 107.04 units.

Calculate the Area of a Circle with a Circumference of 107.04 Units

What does "Calculate the area of a circle with a circumference of 107.04 units" mean? Understand first

When we are asked to calculate the area of a circle with a given circumference of 107.04 units, we are essentially being asked to find the amount of space enclosed within the circle. The circumference is the distance around the circle, while the area is the measure of the space inside the circle.

What is the answer to "Calculate the area of a circle with a circumference of 107.04 units"? Give the answer first

The answer to this problem is the area of the circle, expressed in square units. To find the area, we need to perform some calculations using the given circumference.

The area of the circle with a circumference of 107.04 units is approximately 907.92 square units.

How to solve the problem: hints

There are different methods to solve this problem, depending on the information given. Let's explore three possible methods:

Method 1: If radius is given

1. 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

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

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

2. Plug the circumference of the circle into the formula for 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 107.04 units and finally get the answer, expressed in numbers

To calculate the area of a circle with a circumference of 107.04 units, we can use any of the three methods mentioned above. Let's assume we are given the circumference and use Method 3:

1. 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

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

   • A = π * (107.04 / (2π))^2

3. Simplify the equation.

   • A = π * (53.52 / π)^2
   • A = π * (53.52^2 / π^2)
   • A = (π * 53.52^2) / π^2

4. Cancel out the π terms.

   • A = 53.52^2 / π

5. Calculate the area using the given circumference.

   • A ≈ 907.92 square units

Therefore, the area of the circle with a circumference of 107.04 units is approximately 907.92 square units.

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. The distance from the center of the circle to any point on its boundary is called the radius, and the distance around the circle is called the circumference.

How to draw a circle?

To draw a circle, you need a compass and a pencil. Follow these steps:

1. Place the pointed end of the compass at the center point where you want the circle to be.
2. Adjust the other end of the compass to the desired radius length.
3. Keeping the compass steady, rotate it 360 degrees around the center point, making sure the pencil traces a complete 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 boundary.
• Diameter: The distance across the circle, passing through the center point and touching two points on the boundary. It is equal to twice the radius.
• Circumference: The distance around the circle. It is equal to π times the diameter or 2π times the radius.
• Area: The measure of the space 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, meaning it cannot be expressed as a simple fraction and its decimal representation goes on forever without repeating. The approximate value of pi is 3.14159, but it is often rounded to 3.14 for simplicity in calculations.

The origin of Π?

The origin of the symbol Π (pi) can be traced back to ancient Greece. The Greek mathematician Archimedes is often credited with the first accurate calculation of pi. The symbol Π was later introduced by the Welsh mathematician William Jones in 1706, who used it to represent the ratio of the circumference to the diameter of a circle.

Frequently asked questions about circles

Question: Calculate the area of a circle with a circumference of 107.04 units.

Answer: The area of the circle with a circumference of 107.04 units is approximately 907.92 square units.