Determine the area of a circle with a diameter of 14 inches.

Determine the Area of a Circle with a Diameter of 14 inches

What does "Determine the area of a circle with a diameter of 14 inches" 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 14 inches. 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 14 inches is approximately 153.94 square inches.

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 = 14/2 = 7 inches

3. Finally, calculate the area using the formula:

   • A = π * (7)^2 = 22/7 * 49 ≈ 153.94 square inches

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 = 14 inches

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

   • d = 14 inches

3. Calculate the radius using the formula:

   • r = d/2 = 14/2 = 7 inches

4. Finally, calculate the area using the formula:

   • A = π * (7)^2 = 22/7 * 49 ≈ 153.94 square inches

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 = 2 * π * r
   • r = C / (2 * π)

3. Finally, calculate the area using the formula:

   • A = π * (r)^2 = π * (C / (2 * π))^2 = C^2 / (4 * π) ≈ 153.94 square inches

Step by step solution to Determine the area of a circle with a diameter of 14 inches and finally get the answer, expressed in numbers.

1. Calculate the radius using the formula: r = d/2 = 14/2 = 7 inches.
2. Plug the radius into the formula for the area of a circle: A = π * (7)^2 = 22/7 * 49 ≈ 153.94 square inches.

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 pressed against 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 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 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 is often credited with the first accurate calculation of pi. The symbol Π was later introduced by the Welsh mathematician William Jones in 1706, who used it to represent the ratio of a circle's circumference to its diameter.

Frequently asked questions about circles

Question: Determine the area of a circle with a diameter of 14 inches.

Answer: The area of a circle with a diameter of 14 inches is approximately 153.94 square inches.