Calculate the area of a circle with a circumference of 94.2 meters.

Calculate the Area of a Circle with a Circumference of 94.2 Meters

What does "Calculate the area of a circle with a circumference of 94.2 meters" mean? Understand first

To understand the problem, we need to know what a circle is and what its circumference and area represent. A circle is a perfectly round shape with all points equidistant from the center. The circumference of a circle is the distance around its outer edge, while the area of a circle is the measure of the space enclosed by the circle.

What is the answer to "Calculate the area of a circle with a circumference of 94.2 meters"? Give the answer first

The answer to the problem is the area of the circle. To calculate it, we need to use the given circumference of 94.2 meters.

Answer: The area of the circle with a circumference of 94.2 meters is approximately 282.74 square meters.

How to solve the problem: hints

There are multiple methods to solve this problem, depending on the information given. We will discuss 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

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

   • A = π * (C / (2π))^2

3. Finally, calculate the answer by substituting the given circumference into the formula and expressing the result 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, substituting the given circumference into the formula, and express the result 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 answer by substituting the given circumference into the formula and expressing the result in numbers.

Step by step solution to calculate the area of a circle with a circumference of 94.2 meters and finally get the answer, expressed in numbers

We will use Method 3 since the circumference 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 * (94.2 / (2π))^2

3. Simplify the formula.

   • A = π * (47.1 / π)^2
   • A = π * (47.1^2 / π^2)
   • A = (47.1^2 * π) / π^2
   • A = 47.1^2 / π

4. Calculate the answer using a calculator.

   • A ≈ 282.74 square meters

Therefore, the area of the circle with a circumference of 94.2 meters is approximately 282.74 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. Place the sharp end of the compass at the center point of the circle and rotate the other arm around it. 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 edge.
• Diameter: The distance across the circle, passing through the center and touching two points on the edge. It is twice the length of the radius.
• Circumference: The distance around the outer edge of the circle. It is equal to π times the diameter or 2π times the radius.
• Area: The measure of the space enclosed by the circle.

What does Π mean?

The symbol Π (pi) represents the mathematical constant that represents the ratio of a circle's circumference 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 the ancient Greek mathematician Archimedes. He used the Greek letter π as an abbreviation for the word "periphery" or "circumference" in his mathematical works. The symbol was later adopted by other mathematicians and became widely used to represent the mathematical constant we know today.

Frequently asked questions about circles

Question: Calculate the area of a circle with a circumference of 94.2 meters.

Answer: The area of the circle with a circumference of 94.2 meters is approximately 282.74 square meters.