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 M 2 49 \pi \, M^2 49 Π M 2
Introduction
In mathematics, the area of a circle is a fundamental concept that is used to calculate the size of a circle. The area of a circle is determined by its radius or diameter. In this article, we will explore how to calculate the area of a circle using its diameter. We will use a real-life example to illustrate the concept.
What is the Area of a Circle?
The area of a circle is the amount of space inside the circle. It is measured in square units, such as square meters (m^2) or square feet (ft^2). The area of a circle 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 this article, we will use the diameter of the circle to calculate its area. The diameter of a circle is twice the radius. Therefore, we 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.
Example: Fiona Draws a Circle with a Diameter of 14 Meters
Let's use the example given in the problem statement. 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) into the formula:
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, the area of a circle can be calculated using its diameter. By using the formula A = π(d/2)^2, we can calculate the area of a circle given its diameter. In this article, we used a real-life example to illustrate the concept. We calculated the area of a circle with a diameter of 14 meters and found that the area is 49π square meters.
Answer
The correct answer is D. .
Additional Tips and Tricks
- To calculate the area of a circle using its radius, use the formula A = πr^2.
- To calculate the area of a circle using its diameter, use the formula A = π(d/2)^2.
- Make sure to use the correct units when calculating the area of a circle. In this article, we used square meters (m^2) as the unit of measurement.
Real-World Applications
The concept of calculating the area of a circle has many real-world applications. For example:
- Architects use the area of a circle to calculate the size of a circular building or a circular room.
- Engineers use the area of a circle to calculate the size of a circular pipe or a circular tank.
- Geographers use the area of a circle to calculate the size of a circular lake or a circular island.
Conclusion
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: Can I use the diameter of the circle to calculate its area?
A: Yes, you can use the diameter of the circle to calculate its area. The formula is 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 of the circle. The diameter of a circle is twice the radius, or the distance across the circle passing through its center.
Q: How do I calculate 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) into the formula, 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 unit of measurement for the area of a circle?
A: The unit of measurement for the area of a circle is typically square units, such as square meters (m^2) or square feet (ft^2).
Q: Can I use the area of a circle to calculate its diameter?
A: Yes, you can use the area of a circle to calculate its diameter. Rearranging the formula A = πr^2 to solve for r, you get:
r = √(A/π)
Once you have the value of the radius, you can calculate the diameter by multiplying the radius by 2.
Q: What are some real-world applications of calculating the area of a circle?
A: Some real-world applications of calculating the area of a circle include:
- Architects use the area of a circle to calculate the size of a circular building or a circular room.
- Engineers use the area of a circle to calculate the size of a circular pipe or a circular tank.
- Geographers use the area of a circle to calculate the size of a circular lake or a circular island.
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 value of the radius or diameter into the calculator, and it will give you the area of the circle.
Q: What is the significance of the mathematical constant π (pi) in calculating the area of a circle?
A: The mathematical constant π (pi) is a fundamental constant in mathematics that is approximately equal to 3.14. It is used in the formula for calculating the area of a circle, and is a key component in many mathematical calculations.
Conclusion
In conclusion, calculating the area of a circle is an important concept in mathematics that has many real-world applications. By using the formula A = πr^2 or A = π(d/2)^2, you can calculate the area of a circle given its radius or diameter. We hope that this article has provided you with a better understanding of the concept and its applications.