Calculate the area of a circle with a circumference of 78.5 centimeters.

Calculate the Area of a Circle with a Circumference of 78.5 Centimeters

What does "Calculate the area of a circle with a circumference of 78.5 centimeters" mean? Understand first

When we are asked to calculate the area of a circle with a given circumference of 78.5 centimeters, we are essentially being asked to find the amount of space enclosed within the circle. The circumference is the distance around the circle, while the area is the measure of the surface inside the circle.

What is the answer to "Calculate the area of a circle with a circumference of 78.5 centimeters"? Give the answer first

The answer to this problem is the area of the circle, expressed in square centimeters. To find the exact value, we need to perform some calculations.

How to solve the problem: hints

There are different 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, 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 78.5 centimeters" and finally get the answer, expressed in numbers

To calculate the area of a circle with a circumference of 78.5 centimeters, we can use the formula for the circumference of a circle:

C = 2πr

where C is the circumference and r is the radius of the circle.

Since we are given the circumference, we can rearrange the formula to solve for the radius:

r = C / (2π)

Substituting the given circumference of 78.5 centimeters into the formula, we have:

r = 78.5 / (2π)

Now that we have the radius, we can use the formula for the area of a circle:

A = πr^2

Substituting the calculated radius into the formula, we have:

A = π * (78.5 / (2π))^2

Simplifying the expression, we get:

A = π * (78.5^2 / (2π)^2)

A = 78.5^2 / (2π)

Evaluating the expression, we find:

A ≈ 1549.03 square centimeters

Therefore, the area of the circle with a circumference of 78.5 centimeters is approximately 1549.03 square centimeters.

What is a circle?

A circle is a two-dimensional geometric shape that is perfectly round and consists of all points in a plane that are equidistant from a fixed center point. It is defined by its radius, diameter, and circumference.

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 adjust the other end to the desired radius. Then, rotate the compass around the center point to create the 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 measure of the surface 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 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 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 78.5 centimeters.

Answer: To calculate the area of a circle with a circumference of 78.5 centimeters, we need to find the radius first. Using the formula C = 2πr, we can solve for the radius. Once we have the radius, we can use the formula A = πr^2 to calculate the area. The final answer will be expressed in square centimeters.