The Area Of A Circle With A Diameter Of 240 Mm Is:A. $75.36 \, \text{cm}^2$ B. $150.72 \, \text{cm}^2$ C. $452.16 \, \text{cm}^2$ D. $1,808.64 \, \text{cm}^2$
Introduction
The area of a circle is a fundamental concept in mathematics, and it is essential to understand the formula and calculations involved. In this article, we will explore the formula for the area of a circle, how to calculate it, and provide examples 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 centimeters (cm²) or square meters (m²). The area of a circle is denoted by the symbol A.
Formula for the Area of a Circle
The formula for the area of a circle is:
A = πr²
Where:
- A is the area of the circle
- π (pi) is a mathematical constant approximately equal to 3.14
- r is the radius of the circle
Calculating the Area of a Circle
To calculate the area of a circle, we need to know the radius of the circle. The radius is half the length of the diameter. If we are given the diameter, we can calculate the radius by dividing the diameter by 2.
Example 1: Calculating the Area of a Circle with a Diameter of 240 mm
Let's calculate the area of a circle with a diameter of 240 mm.
First, we need to convert the diameter from millimeters (mm) to centimeters (cm). There are 10 mm in 1 cm, so:
240 mm ÷ 10 = 24 cm
Now, we can calculate the radius by dividing the diameter by 2:
Radius = 24 cm ÷ 2 = 12 cm
Now, we can calculate the area of the circle using the formula:
A = πr² = 3.14 × (12 cm)² = 3.14 × 144 cm² = 452.16 cm²
Conclusion
In conclusion, the area of a circle is a fundamental concept in mathematics, and it is essential to understand the formula and calculations involved. By using the formula A = πr², we can calculate the area of a circle given the radius. In the example above, we calculated the area of a circle with a diameter of 240 mm, which is equal to 452.16 cm².
Answer
The correct answer is C. .
Additional Examples
Here are a few more examples to illustrate the concept:
- A circle with a diameter of 180 mm has an area of: A = πr² = 3.14 × (9 cm)² = 3.14 × 81 cm² = 254.34 cm²
- A circle with a diameter of 300 mm has an area of: A = πr² = 3.14 × (15 cm)² = 3.14 × 225 cm² = 706.5 cm²
Conclusion
Introduction
In our previous article, we explored the formula and calculations involved in finding the area of a circle. In this article, we will answer some frequently asked questions about the area of a circle.
Q: What is the formula for the area of a circle?
A: The formula for the area of a circle is:
A = πr²
Where:
- A is the area of the circle
- π (pi) is a mathematical constant approximately equal to 3.14
- r is the radius of the circle
Q: How do I calculate the area of a circle if I only know the diameter?
A: To calculate the area of a circle if you only know the diameter, you need to first calculate the radius by dividing the diameter by 2. Then, you can use the formula A = πr² to calculate the area.
Q: What is the difference between the diameter and the radius of a circle?
A: The diameter of a circle is the distance across the circle, passing through its center. The radius of a circle is the distance from the center of the circle to the edge. The radius is half the length of the diameter.
Q: Can I use the formula A = πd² to calculate the area of a circle?
A: No, you cannot use the formula A = πd² to calculate the area of a circle. This formula is incorrect and will give you an incorrect answer. The correct formula is A = πr².
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 square units, such as square centimeters (cm²) or square meters (m²).
Q: Can I calculate the area of a circle if I only know the circumference?
A: No, you cannot calculate the area of a circle if you only know the circumference. You need to know the radius or diameter to calculate the area.
Q: How do I convert the diameter of a circle from millimeters to centimeters?
A: To convert the diameter of a circle from millimeters to centimeters, you need to divide the diameter in millimeters by 10.
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 and the calculator will give you the area.
Conclusion
In conclusion, we hope this Q&A article has provided you with a better understanding of the area of a circle. If you have any more questions, feel free to ask.
Additional Resources
Frequently Asked Questions
- What is the formula for the area of a circle?
- How do I calculate the area of a circle if I only know the diameter?
- What is the difference between the diameter and the radius of a circle?
- Can I use the formula A = πd² to calculate the area of a circle?
- What is the unit of measurement for the area of a circle?
- Can I calculate the area of a circle if I only know the circumference?
- How do I convert the diameter of a circle from millimeters to centimeters?
- Can I use a calculator to calculate the area of a circle?