Calculate the area of a circle with a circumference of 31.4 units.

Calculate the Area of a Circle with a Circumference of 31.4 Units

What does "Calculate the area of a circle with a circumference of 31.4 units" 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.

The problem asks us to find the area of a circle with a given circumference of 31.4 units.

What is the answer to "Calculate the area of a circle with a circumference of 31.4 units"? Give the answer first

The answer to the problem is the area of the circle.

How to solve the problem: hints

There are different 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.
2. Plug the radius of the circle into the formula.
3. Finally, get the answer, expressed in numbers.

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.
4. Finally, get the answer, expressed 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.
2. Plug the circumference of the circle into the formula.
3. Finally, get the answer, expressed in numbers.

Step by step solution to calculate the area of a circle with a circumference of 31.4 units and finally get the answer, expressed in numbers

To calculate the area of a circle with a circumference of 31.4 units, we can 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

2. Plug the circumference of the circle into the formula for circumference: 31.4 = 2πr

3. Solve for the radius (r): Divide both sides of the equation by 2π: r = 31.4 / (2π)

4. Finally, calculate the area using the formula for the area of a circle: A = πr^2 Substitute the value of r: A = π * (31.4 / (2π))^2

5. Simplify the expression: A = π * (31.4^2 / (2π)^2) A = π * (31.4^2 / 4π^2) A = (31.4^2 / 4π)

6. Calculate the value of the expression using a calculator: A ≈ 246.3 square units

Therefore, the area of a circle with a circumference of 31.4 units is approximately 246.3 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.

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. 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 edge.
• Diameter: The distance across the circle, passing through the center and touching two points on the edge. It is equal to twice 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. It is equal to π times the square of the radius.

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. 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 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 31.4 units.

To calculate the area of a circle with a circumference of 31.4 units, we can use the formula A = πr^2. By solving the equation step by step, we find that the area is approximately 246.3 square units.