Determine the area of a circle with a diameter of 16 inches.

Determine the Area of a Circle with a Diameter of 16 inches

What does "Determine the area of a circle with a diameter of 16 inches" mean?

This math problem is asking us to find the area of a circle when the diameter is given. The diameter is the distance across the circle passing through the center. In this case, the diameter is 16 inches.

Answer:

The area of a circle with a diameter of 16 inches is approximately 201.06 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 = 16/2 = 8 inches

3. Calculate the area using the formula:

   • A = π * (8)^2

4. 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:

   • Area of a circle: A = π * r^2
   • Diameter of a circle: d = 16 inches

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

   • d = 16 inches

3. Calculate the radius using the formula:

   • r = d/2

4. Calculate the area using the formula:

   • A = π * (r)^2

5. 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:

   • 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 = 16π inches

3. Calculate the radius using the formula:

   • r = C / (2π)

4. Calculate the area using the formula:

   • A = π * (r)^2

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

Step by step solution to Determine the area of a circle with a diameter of 16 inches and finally get the answer, expressed in numbers.

1. Calculate the radius using the formula:

   • r = 16/2 = 8 inches

2. Calculate the area using the formula:

   • A = π * (8)^2

3. Substitute the value of π (pi) as approximately 3.14159:

   • A = 3.14159 * (8)^2

4. Calculate the square of 8:

   • A = 3.14159 * 64

5. Multiply π by 64:

   • A ≈ 201.06 square inches

Therefore, the area of a circle with a diameter of 16 inches is approximately 201.06 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. Place the sharp end of the compass at the center point of the circle and rotate the other end around it. This will create a perfect circle.

What data does the circle have?

A circle has several important measurements:

• Diameter: The distance across the circle passing through the center.
• Radius: The distance from the center of the circle to any point on its circumference.
• Circumference: The distance around the circle.
• Area: The amount of space enclosed by 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.

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 16 inches.

Answer: The area of a circle with a diameter of 16 inches is approximately 201.06 square inches.