Fiona Draws A Circle With A Diameter Of 14 Meters. What Is The Area Of Fiona's Circle?A. $7 \pi , \text{m}^2$ B. $14 \pi , \text{m}^2$ C. $ 28 Π M 2 28 \pi \, \text{m}^2 28 Π M 2 [/tex] D. $49 \pi , \text{m}^2$
Introduction
In mathematics, the area of a circle is a fundamental concept that is used to calculate the amount of space inside a circular shape. The area of a circle is determined by its radius or diameter, and it is an essential concept in various fields such as geometry, trigonometry, and engineering. In this article, we will explore the concept of the area of a circle and provide a step-by-step guide on how to calculate it.
What is the Area of a Circle?
The area of a circle is the amount of space inside the circle, and it is measured in square units. The area of a circle is denoted by the symbol A, and it is calculated using the formula:
A = πr^2
where A is the area of the circle, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
Calculating the Area of a Circle Using the Diameter
In the problem presented, Fiona draws a circle with a diameter of 14 meters. To calculate the area of the circle, we need to first find the radius of the circle. The radius of a circle is half of its diameter, so we can calculate the radius as follows:
Radius = Diameter / 2 = 14 / 2 = 7 meters
Now that we have the radius, we can calculate the area of the circle using the formula:
A = πr^2 = π(7)^2 = 3.14(49) = 154.06 square meters
However, the options provided in the problem do not include the exact value of 154.06 square meters. Instead, they provide approximate values in terms of π. To determine the correct answer, we need to simplify the expression and express it in terms of π.
Simplifying the Expression
To simplify the expression, we can multiply the radius by itself:
(7)^2 = 49
Now, we can multiply the result by π:
A = π(49) = 49π
Therefore, the area of Fiona's circle is approximately 49π square meters.
Conclusion
In conclusion, the area of a circle is a fundamental concept in mathematics that is used to calculate the amount of space inside a circular shape. To calculate the area of a circle, we need to know its radius or diameter, and we can use the formula A = πr^2 to calculate it. In the problem presented, Fiona draws a circle with a diameter of 14 meters, and we calculated the area of the circle to be approximately 49π square meters.
Final Answer
The final answer is:
- D. 49π m^2
Additional Resources
For more information on the area of a circle, you can refer to the following resources:
- Khan Academy: Area of a Circle
- Math Open Reference: Area of a Circle
- Wolfram MathWorld: Area of a Circle
Discussion
Introduction
In our previous article, we explored the concept of the area of a circle and provided a step-by-step guide on how to calculate it. However, we received many questions from readers who were still unsure about how to calculate the area of a circle. In this article, we will address some of the most frequently asked questions about calculating the area of a circle.
Q: What is the formula for calculating the area of a circle?
A: The formula for calculating the area of a circle is:
A = πr^2
where A is the area of the circle, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
Q: How do I calculate the radius of a circle if I only know its diameter?
A: To calculate the radius of a circle, you can simply divide the diameter by 2:
Radius = Diameter / 2
For example, if the diameter of a circle is 14 meters, the radius would be:
Radius = 14 / 2 = 7 meters
Q: What if I don't know the radius or diameter of the circle? How can I still calculate its area?
A: If you don't know the radius or diameter of the circle, you can use the formula for the area of a circle in terms of the circumference:
A = (C^2) / (4π)
where C is the circumference of the circle.
Q: How do I calculate the circumference of a circle?
A: The circumference of a circle is calculated using the formula:
C = 2πr
where C is the circumference of the circle, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
Q: What if I want to calculate the area of a circle with a diameter of 20 meters? How do I do it?
A: To calculate the area of a circle with a diameter of 20 meters, you can first calculate the radius:
Radius = Diameter / 2 = 20 / 2 = 10 meters
Then, you can use the formula for the area of a circle:
A = πr^2 = π(10)^2 = 3.14(100) = 314 square meters
Q: Can I use a calculator to calculate the area of a circle?
A: Yes, you can use a calculator to calculate the area of a circle. Simply enter the radius or diameter of the circle and the calculator will give you the area.
Q: What if I want to calculate the area of a circle with a radius of 5 meters? How do I do it?
A: To calculate the area of a circle with a radius of 5 meters, you can use the formula for the area of a circle:
A = πr^2 = π(5)^2 = 3.14(25) = 78.5 square meters
Conclusion
In conclusion, calculating the area of a circle is a simple process that requires only a few steps. By using the formula A = πr^2, you can calculate the area of a circle with ease. We hope that this article has helped to clarify any questions you may have had about calculating the area of a circle.
Additional Resources
For more information on calculating the area of a circle, you can refer to the following resources:
- Khan Academy: Area of a Circle
- Math Open Reference: Area of a Circle
- Wolfram MathWorld: Area of a Circle
Discussion
Do you have any questions about calculating the area of a circle? Share your thoughts and experiences in the comments below!