Determine the area of a circle with a diameter of 12 inches.

Determine the Area of a Circle with a Diameter of 12 inches

What does "Determine the area of a circle with a diameter of 12 inches" mean? Understand first

When we are asked to determine the area of a circle with a diameter of 12 inches, we are being asked to find the amount of space enclosed within the circle. The diameter is the distance across the circle passing through its center, and in this case, it is given as 12 inches.

What is the answer to "Determine the area of a circle with a diameter of 12 inches"? Give the answer first

The answer to this problem is the area of the circle, which can be calculated using the formula A = πr^2. In this case, since we are given the diameter, we can find the radius by dividing the diameter by 2. Therefore, the radius is 6 inches. Plugging this value into the formula, we get:

A = π(6)^2 = 36π square inches

So, the area of the circle is 36π 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 = d/2, where d is the diameter

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

   • In this case, the radius is 6 inches.

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

   • The area of the circle is 36π 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 = πr^2
   • Diameter of a circle: d = 2r, where r is the radius

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

   • In this case, the diameter is 12 inches, so the radius is 6 inches.

3. Calculate step by step.

   • Square the radius: 6^2 = 36
   • Multiply by π: 36π

4. Finally, get the answer, expressed in numbers.

   • The area of the circle is 36π 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 = πr^2
   • Circumference of a circle: C = 2πr, where r is the radius

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

   • In this case, the circumference is not given, so we cannot use this method.

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

   • N/A

Step by step solution to "Determine the area of a circle with a diameter of 12 inches" and finally get the answer, expressed in numbers

1. Calculate the radius by dividing the diameter by 2.

   • Radius = 12 inches / 2 = 6 inches

2. Use the formula A = πr^2 to calculate the area.

   • A = π(6)^2 = 36π square inches

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

   • The area of the circle is 36π 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 often represented by a curved line that forms a closed loop.

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, called the needle, while the other arm has a pencil or pen attached to it. Follow these steps:

1. Place the needle of the compass at the center point where you want the circle to be.
2. Adjust the other arm of the compass to the desired radius length.
3. Keeping the needle fixed at the center, rotate the compass 360 degrees around the center point.
4. The pencil or pen will trace out a perfect circle.

What data does the circle have?

A circle has several important measurements and properties:

• 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 equal to twice the radius.
• Circumference: The distance around the circle.
• Area: The amount of space enclosed within 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, meaning it cannot be expressed as a simple fraction or a finite decimal. The approximate value of pi is 3.14159, but it extends infinitely without repeating.

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 itself was introduced by the Welsh mathematician William Jones in 1706, who used the Greek letter pi (Π) as an abbreviation for perimeter.

Frequently asked questions about circles

Question: Determine the area of a circle with a diameter of 12 inches.

Answer: The area of a circle with a diameter of 12 inches is 36π square inches.