Determine the area of a circle with a diameter of 18 centimeters.

Determine the Area of a Circle with a Diameter of 18 Centimeters

What does "Determine the area of a circle with a diameter of 18 centimeters" mean?

This math problem is asking us to find the area of a circle when we are given its diameter. The diameter is the distance across the circle passing through its center, and in this case, it is given as 18 centimeters. The area of a circle is the measure of the region enclosed by the circle's circumference.

Answer:

The area of a circle with a diameter of 18 centimeters is approximately 254.47 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.

   • Area of a circle: A = π * r^2
   • Radius of a circle: r = d/2 (where d is the diameter)

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

   • In this case, the radius would be 18/2 = 9 centimeters.

3. Finally, calculate the area using the formula and express the answer 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 = π * r^2
   • Diameter of a circle: d = 2 * r (where r is the radius)

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

   • In this case, the diameter is given as 18 centimeters.

3. Calculate step by step using the formula to find the radius and then the area.

4. Finally, express the answer 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 = π * r^2
   • Circumference of a circle: C = 2 * π * r (where r is the radius)

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

3. Finally, calculate the area using the formula and express the answer in numbers.

Step by step solution to Determine the area of a circle with a diameter of 18 centimeters and finally get the answer, expressed in numbers.

1. Method 2 is the most straightforward approach since we are given the diameter directly.

2. Using the formula for the diameter of a circle, we find that the radius is 18/2 = 9 centimeters.

3. Now, we can use the formula for the area of a circle to calculate the area.

   • A = π * r^2
   • A = π * 9^2
   • A ≈ 254.47 square centimeters

4. Therefore, the area of a circle with a diameter of 18 centimeters is approximately 254.47 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. The distance from the center of the circle to any point on its boundary is called the radius, and the distance across the circle passing through its center is called the diameter.

How to draw a circle?

To draw a circle, you will need a compass and a pencil. Follow these steps:

1. Place the pointed end of the compass on the paper where you want the center of the circle to be.

2. Adjust the other end of the compass to the desired radius length.

3. Keeping the compass steady, rotate it 360 degrees around the center point, making sure the pencil traces a complete circle.

4. Finally, you will have a perfectly drawn 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 its center. It is twice the length of the radius.
• Circumference: The distance around the circle.
• Area: The measure of the region enclosed by the circle's circumference.

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, such as calculating the circumference and area.

The origin of Π

The symbol Π comes from the Greek word "pi" (pronounced "pee"), which is the first letter of the Greek word "periphery." The use of Π to represent the mathematical constant pi was introduced by the Welsh mathematician William Jones in 1706, and it has been widely adopted ever since.

Frequently asked questions about circles

Question: Determine the area of a circle with a diameter of 18 centimeters.

Answer: The area of a circle with a diameter of 18 centimeters is approximately 254.47 square centimeters.