Calculate the area of a circle with a circumference of 78.54 centimeters.

Calculate the Area of a Circle with a Circumference of 78.54 Centimeters

What does "Calculate the area of a circle with a circumference of 78.54 centimeters" 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. In this case, the circumference of the circle is given as 78.54 centimeters.

What is the answer to "Calculate the area of a circle with a circumference of 78.54 centimeters"? Give the answer first

The answer to this problem is the area of the circle, which is approximately 198.96 square centimeters.

How to solve the problem: hints

There are multiple methods to solve this problem, depending on the information given. Here are three 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 of the circle.
2. Plug the radius of the circle into the formula.
3. Finally, calculate the area using the formula 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 of the circle.
2. Plug the diameter of the circle into the formula.
3. Calculate step by step.
4. Finally, calculate the area using the formula 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 of the circle.
2. Plug the circumference of the circle into the formula.
3. Finally, calculate the area using the formula and express the answer in numbers.

Step by step solution to "Calculate the area of a circle with a circumference of 78.54 centimeters" and finally get the answer, expressed in numbers

Since the circumference of the circle is given, we will use Method 3 to solve this problem.

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
2. Plug the circumference of the circle into the formula.
   • C = 2πr
   • 78.54 = 2πr
3. Solve for the radius (r).
   • Divide both sides of the equation by 2π: r = 78.54 / (2π)
4. Finally, calculate the area using the formula.
   • A = πr^2
   • A = π(78.54 / (2π))^2
   • A ≈ 198.96 square centimeters

Therefore, the area of the circle with a circumference of 78.54 centimeters is approximately 198.96 square centimeters.

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, called the needle, while the other arm holds a pencil or pen. Follow these steps:

1. Place the needle of the compass at the center point where you want the circle to be.
2. Adjust the other arm of the compass to the desired radius length.
3. Keeping the needle at the center point, rotate the compass 360 degrees around the center, ensuring that the pencil or pen traces a complete circle.

What data does the circle have?

A circle has several important measurements:

• Radius (r): The distance from the center of the circle to any point on its circumference.
• Diameter (d): The distance across the circle, passing through the center and touching two points on the circumference. It is equal to twice the radius.
• Circumference (C): The distance around the circle. It is equal to π times the diameter or 2π times the radius.
• Area (A): The amount of space enclosed within the circle.

What does Π mean?

The symbol Π (pi) represents the mathematical constant that represents the ratio of the circumference of any circle to its diameter. It is an irrational number, approximately equal to 3.14159. Pi is used in many mathematical formulas involving circles and is a fundamental constant in mathematics.

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 perimeter.

Frequently asked questions about circles

Question: Calculate the area of a circle with a circumference of 78.54 centimeters.

Answer: The area of a circle with a circumference of 78.54 centimeters is approximately 198.96 square centimeters.