Calculate the area of a circle with a circumference of 100 centimeters.

Calculate the Area of a Circle with a Circumference of 100 Centimeters

What does "Calculate the area of a circle with a circumference of 100 centimeters" mean? Understand first

To calculate the area of a circle with a circumference of 100 centimeters means finding the amount of space enclosed within the circle when the distance around its boundary is 100 centimeters.

What is the answer to "Calculate the area of a circle with a circumference of 100 centimeters"? Give the answer first

The answer is approximately 796.81 square centimeters.

How to solve the problem: hints

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 100 centimeters" and finally get the answer, expressed in numbers

To calculate the area of a circle with a circumference of 100 centimeters, we can use Method 3 mentioned above.

1. The formula for calculating 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 100 centimeters: r = 100 / (2π).
4. Calculate the value of r using a calculator: r ≈ 15.92 centimeters.
5. The formula for calculating the area of a circle is: A = πr^2, where A is the area and r is the radius.
6. Plug in the calculated radius: A = π(15.92)^2.
7. Calculate the value of A using a calculator: A ≈ 796.81 square centimeters.
8. The answer to the problem is approximately 796.81 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 has a pencil or pen attached to it. 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 fixed at the center, rotate the pencil or pen around the center point, creating 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 boundary.
• Diameter: The distance across the circle, passing through the center and touching two points on the boundary. It is equal to twice the radius.
• Circumference: The distance around the boundary of the circle. It is equal to π times the diameter or 2π times the radius.
• Area: 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.

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, which is the first letter of the Greek word "periphery," to represent the circumference of a circle.

Frequently asked questions about circles

Question: Calculate the area of a circle with a circumference of 100 centimeters.

To calculate the area of a circle with a circumference of 100 centimeters, you can use the formulas mentioned above. By plugging in the given circumference into the appropriate formula, you can find the radius and then calculate the area using the formula A = πr^2. The answer will be expressed in square centimeters.