Determine the area of a circle with a diameter of 10 inches.

Determine the Area of a Circle with a Diameter of 10 inches

What does "Determine the area of a circle with a diameter of 10 inches" mean? Understand first

When we are asked to determine the area of a circle with a diameter of 10 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 10 inches.

What is the answer to "Determine the area of a circle with a diameter of 10 inches"? Give the answer first

The answer to this problem is the area of the circle, which can be calculated using the formula:

Area = π * (radius)^2

In this case, since the diameter is given, we can find the radius by dividing the diameter by 2. Therefore, the radius is 5 inches.

Plugging the radius into the formula, we get:

Area = π * (5 inches)^2

Simplifying further, we have:

Area = π * 25 square inches

So, the area of the circle with a diameter of 10 inches is 25π 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.
2. Plug the radius of the circle into the formula.
3. Finally, get the answer, expressed in numbers.

Method 2: If diameter is given

1. List the formulas for calculating the area and diameter of a circle.
2. Plug the diameter of the circle into the formula.
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.
2. Plug the circumference of the circle into the formula.
3. Finally, get the answer, expressed in numbers.

Step by step solution to "Determine the area of a circle with a diameter of 10 inches" and finally get the answer, expressed in numbers

1. Calculate the radius by dividing the diameter by 2. In this case, the radius is 5 inches.
2. Use the formula for the area of a circle: Area = π * (radius)^2.
3. Plug in the value of the radius: Area = π * (5 inches)^2.
4. Simplify the expression: Area = π * 25 square inches.
5. The final answer is 25π 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, and 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 at the center point, rotate the compass 360 degrees to draw a complete circle.

What data does the circle have?

A circle has several important measurements:

• Diameter: The distance across the circle passing through its center.
• Radius: Half the length of the diameter. It is the distance from the center to any point on the circle.
• 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 the circumference of any circle 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 Greece. The Greek mathematician Archimedes is often credited with the discovery and calculation of pi. The symbol Π was later introduced by the Welsh mathematician William Jones in 1706.

Frequently asked questions about circles

Question: Determine the area of a circle with a diameter of 10 inches.

Answer: The area of a circle with a diameter of 10 inches is 25π square inches.