Fiona Draws A Circle With A Diameter Of 14 Meters. What Is The Area Of Fiona's Circle?A. 7 Π M 2 7 \pi \, M^2 7 Π M 2 B. 14 Π M 2 14 \pi \, M^2 14 Π M 2 C. 28 Π M 2 28 \pi \, M^2 28 Π M 2 D. 49 Π 2 M 2 49 \pi^2 \, M^2 49 Π 2 M 2
Introduction
In mathematics, the area of a circle is a fundamental concept that is used to calculate the size of a circular region. The area of a circle is determined by its radius or diameter, and it is an essential concept in geometry and trigonometry. In this article, we will explore how to calculate the area of a circle using its diameter, and we will use a real-world example to illustrate the concept.
What is the Area of a Circle?
The area of a circle is a measure of the size of the circular region. 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
However, in many cases, we are given the diameter of the circle instead of the radius. In such cases, we can use the following formula to calculate the area of the circle:
A = π(d/2)^2
where A is the area of the circle, π (pi) is a mathematical constant approximately equal to 3.14, and d is the diameter of the circle.
Real-World Example: Fiona's Circle
Let's consider a real-world example to illustrate the concept. Fiona draws a circle with a diameter of 14 meters. We want to calculate the area of Fiona's circle.
Using the formula A = π(d/2)^2, we can plug in the value of the diameter (14 meters) to calculate the area of the circle:
A = π(14/2)^2 A = π(7)^2 A = π(49) A = 49π
Therefore, the area of Fiona's circle is 49π square meters.
Conclusion
In conclusion, calculating the area of a circle is a simple process that involves using the formula A = πr^2 or A = π(d/2)^2. By using these formulas, we can easily calculate the area of a circle given its radius or diameter. In this article, we used a real-world example to illustrate the concept and calculated the area of Fiona's circle using the diameter.
Answer
The correct answer is C. . However, the correct calculation is .
Why is the answer not C?
The answer is not C because the correct calculation is . The correct answer is not among the options provided.
Why is the answer not D?
The answer is not D because the correct calculation is , not .
Why is the answer not A?
The answer is not A because the correct calculation is , not .
Why is the answer not B?
The answer is not B because the correct calculation is , not .
Final Answer
Introduction
In our previous article, we explored how to calculate the area of a circle using its diameter. We used a real-world example to illustrate the concept and calculated the area of Fiona's circle. In this article, we will provide a Q&A guide to help you understand the concept better.
Q: What is the formula to calculate the area of a circle?
A: The formula to calculate 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 area of a circle using the diameter?
A: To calculate the area of a circle using the diameter, you can use the formula A = π(d/2)^2, where A is the area of the circle, π (pi) is a mathematical constant approximately equal to 3.14, and d is the diameter of the circle.
Q: What is the difference between the radius and the diameter of a circle?
A: The radius of a circle is the distance from the center of the circle to the edge, while the diameter is the distance across the circle passing through its center. In other words, the diameter is twice the radius.
Q: How do I calculate the radius of a circle given its diameter?
A: To calculate the radius of a circle given its diameter, you can use the formula r = d/2, where r is the radius of the circle and d is the diameter of the circle.
Q: What is the area of a circle with a diameter of 10 meters?
A: To calculate the area of a circle with a diameter of 10 meters, you can use the formula A = π(d/2)^2. Plugging in the value of the diameter (10 meters), you get:
A = π(10/2)^2 A = π(5)^2 A = π(25) A = 25π
Therefore, the area of the circle is 25π square meters.
Q: What is the area of a circle with a radius of 5 meters?
A: To calculate the area of a circle with a radius of 5 meters, you can use the formula A = πr^2. Plugging in the value of the radius (5 meters), you get:
A = π(5)^2 A = π(25) A = 25π
Therefore, the area of the circle is 25π square meters.
Q: Can I use the formula A = πr^2 to calculate the area of a circle using the diameter?
A: Yes, you can use the formula A = πr^2 to calculate the area of a circle using the diameter. Since the diameter is twice the radius, you can plug in the value of the diameter divided by 2 into the formula.
Q: What is the relationship between the area of a circle and its diameter?
A: The area of a circle is proportional to the square of its diameter. In other words, if the diameter of a circle is doubled, the area of the circle is quadrupled.
Conclusion
In conclusion, calculating the area of a circle is a simple process that involves using the formula A = πr^2 or A = π(d/2)^2. By understanding the relationship between the radius and the diameter of a circle, you can easily calculate the area of a circle given its diameter or radius. We hope this Q&A guide has helped you understand the concept better.