Determine the area of a circle with a diameter of 34 centimeters.

Determine the Area of a Circle with a Diameter of 34 Centimeters

What does "Determine the area of a circle with a diameter of 34 centimeters" mean?

This math problem is asking us to find the area of a circle when the diameter is given. The diameter is the distance across the circle passing through the center. In this case, the diameter is 34 centimeters.

Answer:

The area of a circle with a diameter of 34 centimeters is approximately 907.92 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:

   • r = 34/2 = 17 centimeters

3. Finally, calculate the area using the formula:

   • A = π * (17)^2 = 907.92 square centimeters

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 = 34 centimeters

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

   • d = 34 centimeters

3. Calculate the radius using the formula:

   • r = d/2 = 34/2 = 17 centimeters

4. Finally, calculate the area using the formula:

   • A = π * (17)^2 = 907.92 square centimeters

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

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

   • C = 34π centimeters

3. Calculate the radius using the formula:

   • r = C / (2π) = (34π) / (2π) = 17 centimeters

4. Finally, calculate the area using the formula:

   • A = π * (17)^2 = 907.92 square centimeters

Step by step solution to Determine the area of a circle with a diameter of 34 centimeters

1. Calculate the radius using the formula: r = d/2 = 34/2 = 17 centimeters.
2. Calculate the area using the formula: A = π * (17)^2 = 907.92 square centimeters.

What is a circle?

A circle is a two-dimensional geometric shape that is perfectly round. It is defined as the set of all points in a plane that are equidistant from a fixed center point. The distance from the center to any point on the circle is called the radius, and the distance across the circle passing through the 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 at the center point where you want 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.

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. It is equal to twice the radius.
• Circumference: The distance around the circle.
• Area: The amount of space enclosed by the circle.

What does Π mean?

The symbol Π (pi) represents the mathematical constant that is 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, including the formulas for calculating the area and circumference.

The origin of Π

The symbol Π (pi) has its origin in ancient Greek mathematics. It was first introduced by the Greek mathematician Archimedes and later popularized by the Swiss mathematician Leonhard Euler. The symbol Π comes from the Greek word "perimetros," meaning circumference.

Frequently asked questions about circles

Question: Determine the area of a circle with a diameter of 34 centimeters.

Answer: The area of a circle with a diameter of 34 centimeters is approximately 907.92 square centimeters.