Find the area of a circle with a radius of 12.4 inches.

Find the Area of a Circle with a Radius of 12.4 inches

What does "Find the area of a circle with a radius of 12.4 inches" mean? Understand first

When we are asked to find the area of a circle with a radius of 12.4 inches, 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. In this case, the radius is given as 12.4 inches.

What is the answer to "Find the area of a circle with a radius of 12.4 inches"? Give the answer first

The answer to finding the area of a circle with a radius of 12.4 inches is approximately 483.1 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 = πr^2
   • Radius of a circle: r = √(A/π)
2. Plug the radius of the circle (12.4 inches) into the formula for area.
   • A = π(12.4)^2
3. Finally, calculate the answer, expressed in numbers.
   • A ≈ 483.1 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(d/2)^2
   • Diameter of a circle: d = 2r
2. Plug the diameter of the circle (2 * 12.4 inches) into the formula for area.
   • A = π((2 * 12.4)/2)^2
3. Calculate step by step.
   • A = π(12.4)^2
4. Finally, get the answer, expressed in numbers.
   • A ≈ 483.1 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 = (C^2)/(4π)
   • Circumference of a circle: C = 2πr
2. Plug the circumference of the circle into the formula for area.
   • A = ((2πr)^2)/(4π)
3. Finally, calculate the answer, expressed in numbers.
   • A ≈ 483.1 square inches

Step by step solution to "Find the area of a circle with a radius of 12.4 inches" and finally get the answer, expressed in numbers

Using Method 1:

1. Area of a circle: A = πr^2
2. Plug the radius of the circle (12.4 inches) into the formula for area.
   • A = π(12.4)^2
3. Calculate the answer.
   • A ≈ 483.1 square inches

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 rotate the other end around it, keeping it at a fixed distance (radius) from the center. This will trace out the circumference of 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, 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 (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, but it can be rounded to 3.14 for most calculations.

The origin of Π?

The origin of the symbol Π (pi) can be traced back to ancient Greek mathematicians. It was first used by the mathematician William Jones in 1706 and later popularized by the Swiss mathematician Leonhard Euler in the 18th century.

Frequently asked questions about circles

Question: Find the area of a circle with a radius of 12.4 inches.

Answer: The area of a circle with a radius of 12.4 inches is approximately 483.1 square inches.