Determine the area of a circle with a diameter of 38 centimeters.

Determine the Area of a Circle with a Diameter of 38 Centimeters

What does "Determine the area of a circle with a diameter of 38 centimeters" mean?

This math problem is asking us to find the area of a circle that has a diameter of 38 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 38 centimeters is approximately 1134.11 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 for area.

   • A = π * (d/2)^2

3. Finally, calculate the answer, expressed 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 for area.

   • A = π * (d/2)^2

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.

   • 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 for area.

   • A = (C^2) / (4 * π)

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

Step by step solution to Determine the area of a circle with a diameter of 38 centimeters and finally get the answer, expressed in numbers.

1. Calculate the radius of the circle.

   • Radius (r) = Diameter (d) / 2
   • r = 38 cm / 2
   • r = 19 cm

2. Plug the radius into the formula for area.

   • Area (A) = π * r^2
   • A = π * (19 cm)^2

3. Calculate the area.

   • A ≈ 3.14159 * (19 cm)^2
   • A ≈ 3.14159 * 361 cm^2
   • A ≈ 1134.11 cm^2

4. Finally, the area of the circle with a diameter of 38 centimeters is approximately 1134.11 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 need 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 point 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 region enclosed by the circle's circumference.

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 and is a fundamental constant in mathematics.

The origin of Π?

The origin of the symbol Π (pi) can be traced back to ancient Greece. The Greek mathematician Archimedes was the first to use the symbol to represent the ratio of a circle's circumference to its diameter. The symbol Π comes from the Greek word "periphereia," which means circumference.

Frequently asked questions about circles

Question: Determine the area of a circle with a diameter of 38 centimeters.

Answer: The area of a circle with a diameter of 38 centimeters is approximately 1134.11 square centimeters.