Determine the area of a circle with a diameter of 8 feet.

Determine the Area of a Circle with a Diameter of 8 Feet

What does "Determine the area of a circle with a diameter of 8 feet" mean? Understand first

When we are asked to determine the area of a circle with a diameter of 8 feet, 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 8 feet.

What is the answer to "Determine the area of a circle with a diameter of 8 feet"? 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 the diameter is given, we can find the radius by dividing the diameter by 2. Therefore, the area of the circle with a diameter of 8 feet is approximately 50.27 square feet.

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 (A) = πr^2
   • Radius (r) = Diameter (d) / 2

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

   • A = π(8/2)^2

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

   • A ≈ 3.14 * 4^2 ≈ 3.14 * 16 ≈ 50.27 square feet

Method 2: If diameter is given

1. List the formulas for calculating the area and diameter of a circle:

   • Area (A) = πr^2
   • Diameter (d) = 2r

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

   • A = π(8/2)^2

3. Calculate step by step:

   • A ≈ 3.14 * 4^2 ≈ 3.14 * 16 ≈ 50.27 square feet

Method 3: If the circumference of the circle is given

1. List the formulas for calculating the area and circumference of a circle:

   • Area (A) = πr^2
   • Circumference (C) = 2πr

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

   • C = 2πr
   • r = C / (2π)
   • A = π(C / (2π))^2

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

   • A ≈ 3.14 * (C / (2π))^2

Step by step solution to "Determine the area of a circle with a diameter of 8 feet" and finally get the answer, expressed in numbers

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

   • r = 8 / 2 = 4 feet

2. Plug the radius into the formula for the area of a circle:

   • A = π(4)^2

3. Calculate the answer, expressed in numbers:

   • A ≈ 3.14 * 4^2 ≈ 3.14 * 16 ≈ 50.27 square feet

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 can use 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 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 represents 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 introduced 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: Determine the area of a circle with a diameter of 8 feet.

To determine the area of a circle with a diameter of 8 feet, you can use the formula A = πr^2. First, find the radius by dividing the diameter by 2. Then, plug the radius into the formula and calculate the answer. In this case, the area is approximately 50.27 square feet.