The Circumference Of A Circle Is 69.08 Centimeters. What Is The Circle's Diameter?Use $ \pi \approx 3.14 $ And Round Your Answer To The Nearest Hundredth.
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Introduction
In geometry, the circumference of a circle is the distance around the circle, while the diameter is the distance across the circle, passing through its center. Given the circumference of a circle, we can use the formula to find the diameter. In this article, we will explore how to find the diameter of a circle when its circumference is known.
The Formula for Circumference
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
The Relationship Between Circumference and Diameter
The diameter of a circle is twice the radius. Therefore, we can write the formula for the diameter as:
d = 2r
where d is the diameter and r is the radius.
Finding the Diameter from the Circumference
We are given the circumference of the circle as 69.08 centimeters. We can use the formula for circumference to find the radius:
C = 2πr 69.08 = 2(3.14)r 69.08 = 6.28r
To find the radius, we can divide both sides of the equation by 6.28:
r = 69.08 / 6.28 r = 11.00
Now that we have the radius, we can find the diameter by multiplying the radius by 2:
d = 2r d = 2(11.00) d = 22.00
Rounding the Answer
We are asked to round our answer to the nearest hundredth. Therefore, we will round the diameter to the nearest hundredth:
d ≈ 22.00
Conclusion
In this article, we have shown how to find the diameter of a circle when its circumference is known. We used the formula for circumference and the relationship between circumference and diameter to find the radius and then the diameter. We rounded our answer to the nearest hundredth as requested.
Example Use Case
This formula can be used in various real-world applications, such as:
- Calculating the diameter of a wheel or a gear
- Finding the diameter of a pipe or a tube
- Determining the diameter of a circular object, such as a coin or a ring
Tips and Variations
- Make sure to use the correct value of π (pi) in your calculations.
- If you are given the diameter instead of the circumference, you can use the formula d = 2r to find the radius and then the circumference.
- You can also use the formula C = πd to find the circumference when the diameter is known.
Common Mistakes
- Using the wrong value of π (pi) in your calculations.
- Forgetting to round the answer to the nearest hundredth.
- Not using the correct formula for circumference or diameter.
Further Reading
- For more information on geometry and trigonometry, see the following resources:
- For more practice problems and examples, see the following resources:
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Q: What is the formula for the circumference of a circle?
A: The formula for the circumference of a circle is:
C = 2πr
where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
Q: How do I find the diameter of a circle when its circumference is known?
A: To find the diameter of a circle when its circumference is known, you can use the formula:
d = 2r
where d is the diameter and r is the radius. First, find the radius by dividing the circumference by 2π:
r = C / (2π)
Then, multiply the radius by 2 to find the diameter:
d = 2r
Q: What is the relationship between the circumference and the diameter of a circle?
A: The circumference of a circle is directly proportional to its diameter. The formula for the circumference is:
C = πd
where C is the circumference and d is the diameter.
Q: How do I find the radius of a circle when its diameter is known?
A: To find the radius of a circle when its diameter is known, you can use the formula:
r = d / 2
where r is the radius and d is the diameter.
Q: What is the value of π (pi) used in the formulas for circumference and diameter?
A: The value of π (pi) used in the formulas for circumference and diameter is approximately 3.14. However, you can use other values of π depending on the level of precision required.
Q: Can I use the formula for circumference to find the diameter of a circle?
A: Yes, you can use the formula for circumference to find the diameter of a circle. First, find the radius by dividing the circumference by 2π:
r = C / (2π)
Then, multiply the radius by 2 to find the diameter:
d = 2r
Q: What are some real-world applications of the formulas for circumference and diameter?
A: Some real-world applications of the formulas for circumference and diameter include:
- Calculating the diameter of a wheel or a gear
- Finding the diameter of a pipe or a tube
- Determining the diameter of a circular object, such as a coin or a ring
- Calculating the circumference of a circular object, such as a wheel or a track
Q: What are some common mistakes to avoid when using the formulas for circumference and diameter?
A: Some common mistakes to avoid when using the formulas for circumference and diameter include:
- Using the wrong value of π (pi) in your calculations
- Forgetting to round the answer to the nearest hundredth
- Not using the correct formula for circumference or diameter
Q: Where can I find more information on geometry and trigonometry?
A: You can find more information on geometry and trigonometry at the following resources:
Q: Can I use a calculator to find the circumference and diameter of a circle?
A: Yes, you can use a calculator to find the circumference and diameter of a circle. Simply enter the value of the radius or diameter and the calculator will give you the corresponding value of the circumference or diameter.