Calculate the area of a circle with a circumference of 125.66 units.

Calculate the Area of a Circle with a Circumference of 125.66 Units

What does "Calculate the area of a circle with a circumference of 125.66 units" mean? Understand first

When asked to calculate the area of a circle with a given circumference, we are being asked to find the amount of space enclosed within the circle. The circumference is the distance around the circle, and it is given as 125.66 units.

What is the answer to "Calculate the area of a circle with a circumference of 125.66 units"? Give the answer first

The answer to this problem is the area of the circle, expressed in square units.

How to solve the problem: hints

There are multiple methods to solve this problem, depending on the information given. Here are three possible methods:

Method 1: If radius is given

1. List the formulas for calculating the area and radius of a circle.
2. Plug the radius of the circle into the formula.
3. Finally, calculate the area and express the answer in square units.

Method 2: If diameter is given

1. List the formulas for calculating the area and diameter of a circle.
2. Plug the diameter of the circle into the formula.
3. Calculate step by step to find the radius.
4. Finally, calculate the area and express the answer in square units.

Method 3: If the circumference of the circle is given

1. List the formulas for calculating the area and circumference of a circle.
2. Plug the circumference of the circle into the formula.
3. Finally, calculate the area and express the answer in square units.

Step by step solution to calculate the area of a circle with a circumference of 125.66 units and finally get the answer, expressed in numbers

To calculate the area of a circle with a circumference of 125.66 units, we can use Method 3:

1. The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
2. Rearranging the formula, we have r = C / (2π).
3. Plug in the given circumference of 125.66 units into the formula: r = 125.66 / (2π).
4. Calculate the value of r using a calculator.
5. Once we have the radius, we can use the formula for the area of a circle: A = πr^2.
6. Plug in the calculated radius into the formula: A = π * (radius)^2.
7. Calculate the value of A using a calculator.
8. The final answer is the area of the circle, expressed in square units.

What is a circle?

A circle is a two-dimensional geometric shape that is perfectly round. It is defined as the set of all points in a plane that are equidistant from a fixed center point. The distance from the center to any point on the circle is called the radius.

How to draw a circle?

To draw a circle, you need a compass and a pencil.

1. Place the pointed end of the compass at the center of the circle.
2. Adjust the other end of the compass to the desired radius length.
3. Keeping the pointed end fixed, rotate the compass around in a full circle, making sure the pencil traces a smooth curve.
4. The resulting curve is a 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 amount of 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 approximately equal to 3.14159, but it is an irrational number, meaning it cannot be expressed as a simple fraction.

The origin of Π

The origin of the symbol Π can be traced back to the ancient Greek mathematician Archimedes. He used the letter Π to represent the perimeter of a circle in his mathematical works.

Frequently asked questions about circles

Question: Calculate the area of a circle with a circumference of 125.66 units.

To calculate the area of a circle with a given circumference, we need to know either the radius or the diameter of the circle. With the given information of the circumference, we can use the formulas mentioned earlier to find the radius or diameter, and then calculate the area using the appropriate formula.