Find the area of a circle with a radius of 2.5 centimeters.

Find the Area of a Circle with a Radius of 2.5 Centimeters

What does "Find the area of a circle with a radius of 2.5 centimeters" mean? Understand first

When we are asked to find the area of a circle with a radius of 2.5 centimeters, we are being asked to determine the amount of space enclosed within the boundaries of the circle. The radius is the distance from the center of the circle to any point on its circumference, and in this case, it is given as 2.5 centimeters.

What is the answer to "Find the area of a circle with a radius of 2.5 centimeters"? Give the answer first

The answer to this problem is the area of the circle, which can be calculated using the formula A = πr^2, where A represents the area and r represents the radius. Plugging in the given radius of 2.5 centimeters into the formula, we can calculate the area as follows:

A = π(2.5)^2 A = π(6.25) A ≈ 19.63 square centimeters

Therefore, the area of the circle with a radius of 2.5 centimeters is approximately 19.63 square centimeters.

How to solve the problem: hints

Method 1: If radius is given

1. First, list the formulas for calculating the area and radius of a circle.

   • Area (A) = πr^2
   • Radius (r) = √(A/π)

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

   • A = π(2.5)^2

3. Finally, calculate the answer, expressed in numbers.

   • A ≈ 19.63 square centimeters

Method 2: If diameter is given

1. First, list the formulas for calculating the area and diameter of a circle.

   • Area (A) = π(d/2)^2
   • Diameter (d) = 2r

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

   • A = π(2.5/2)^2

3. Calculate step by step.

   • A = π(1.25)^2
   • A = π(1.5625)

4. Finally, get the answer, expressed in numbers.

   • A ≈ 4.91 square centimeters

Method 3: If the circumference of the circle is given

1. First, list the formulas for calculating the area and circumference of a circle.

   • Area (A) = (C^2)/(4π)
   • Circumference (C) = 2πr

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

   • A = (C^2)/(4π)
   • A = (2π(2.5))^2/(4π)

3. Finally, calculate the answer, expressed in numbers.

   • A ≈ 19.63 square centimeters

Step by step solution to "Find the area of a circle with a radius of 2.5 centimeters" and finally get the answer, expressed in numbers

1. Use the formula A = πr^2.
2. Plug in the given radius of 2.5 centimeters.
   • A = π(2.5)^2
3. Calculate the answer.
   • A ≈ 19.63 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, and the other arm has a pencil or pen attached to it. 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 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 amount of space enclosed within the boundaries of the circle.

What does Π mean?

The symbol Π, pronounced as "pi," represents the mathematical constant that is the ratio of the circumference of any circle to its diameter. It is an irrational number, meaning it cannot be expressed as a simple fraction, and its decimal representation goes on infinitely without repeating. The approximate value of Π is 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: Find the area of a circle with a radius of 2.5 centimeters.

To find the area of a circle with a radius of 2.5 centimeters, we can use the formula A = πr^2. By plugging in the given radius, we can calculate the area as approximately 19.63 square centimeters.