The Circumference Of A Circle Is 21 Π 21\pi 21 Π Cm. What Is The Area, In Square Centimeters? Express Your Answer In Terms Of Π \pi Π .

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Introduction

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The circumference of a circle is given as $21\pi$ cm. In this article, we will explore the relationship between the circumference and the area of a circle. We will use the given circumference to find the radius of the circle and then calculate the area using the formula for the area of a circle.

The Formula for the Circumference of a Circle

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The formula for the circumference of a circle is given by:

$$C = 2\pi r$$

where $C$ is the circumference and $r$ is the radius of the circle.

Finding the Radius of the Circle

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We are given that the circumference of the circle is $21\pi$ cm. We can use the formula for the circumference to find the radius of the circle:

$$21\pi = 2\pi r$$

To solve for $r$, we can divide both sides of the equation by $2\pi$:

$$r = \frac{21\pi}{2\pi}$$

Simplifying the expression, we get:

$$r = \frac{21}{2}$$

The Formula for the Area of a Circle

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The formula for the area of a circle is given by:

$$A = \pi r^2$$

where $A$ is the area and $r$ is the radius of the circle.

Finding the Area of the Circle

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We have found that the radius of the circle is $\frac{21}{2}$ cm. We can use the formula for the area to find the area of the circle:

$$A = \pi \left(\frac{21}{2}\right)^2$$

Simplifying the expression, we get:

$$A = \pi \frac{441}{4}$$

$$A = \frac{441\pi}{4}$$

Conclusion

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In this article, we have explored the relationship between the circumference and the area of a circle. We used the given circumference to find the radius of the circle and then calculated the area using the formula for the area of a circle. The area of the circle is $\frac{441\pi}{4}$ square centimeters.

Final Answer

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The final answer is $\boxed{\frac{441\pi}{4}}$.

Related Topics

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• Circumference of a circle
• Area of a circle
• Radius of a circle
• Formulas for circles

References

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• [1] "Circles" by Math Open Reference. Retrieved 2023-12-01.
• [2] "Area of a Circle" by Math Is Fun. Retrieved 2023-12-01.

Additional Resources

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• Khan Academy: Circumference and Area of a Circle
• Mathway: Circumference and Area of a Circle
• Wolfram Alpha: Circumference and Area of a Circle
  

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Introduction

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In our previous article, we explored the relationship between the circumference and the area of a circle. We used the given circumference to find the radius of the circle and then calculated the area using the formula for the area of a circle. In this article, we will answer some frequently asked questions related to the circumference and area of a circle.

Q&A

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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 given by:

$$C = 2\pi r$$

where $C$ is the circumference and $r$ is the radius of the circle.

Q: How do I find the radius of a circle if I know its circumference?

A: To find the radius of a circle, you can use the formula for the circumference:

$$C = 2\pi r$$

Rearranging the formula to solve for $r$, we get:

$$r = \frac{C}{2\pi}$$

Q: What is the formula for the area of a circle?

A: The formula for the area of a circle is given by:

$$A = \pi r^2$$

where $A$ is the area and $r$ is the radius of the circle.

Q: How do I find the area of a circle if I know its radius?

A: To find the area of a circle, you can use the formula for the area:

$$A = \pi r^2$$

Q: What is the relationship between the circumference and the area of a circle?

A: The circumference of a circle is directly proportional to its radius, while the area of a circle is proportional to the square of its radius. This means that as the radius of a circle increases, its circumference increases linearly, but its area increases quadratically.

Q: Can I use the circumference to find the area of a circle?

A: Yes, you can use the circumference to find the area of a circle. First, find the radius of the circle using the formula for the circumference:

$$r = \frac{C}{2\pi}$$

Then, use the formula for the area to find the area of the circle:

$$A = \pi r^2$$

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 use the area to find the circumference of a circle?

A: Yes, you can use the area to find the circumference of a circle. First, find the radius of the circle using the formula for the area:

$$r = \sqrt{\frac{A}{\pi}}$$

Then, use the formula for the circumference to find the circumference of the circle:

$$C = 2\pi r$$

Conclusion

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In this article, we have answered some frequently asked questions related to the circumference and area of a circle. We have explored the formulas for the circumference and area of a circle, and we have discussed how to use these formulas to find the radius and area of a circle.

Final Answer

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The final answer is $\boxed{\frac{441\pi}{4}}$.

Related Topics

---

• Circumference of a circle
• Area of a circle
• Radius of a circle
• Formulas for circles

References

---

• [1] "Circles" by Math Open Reference. Retrieved 2023-12-01.
• [2] "Area of a Circle" by Math Is Fun. Retrieved 2023-12-01.

Additional Resources

---

• Khan Academy: Circumference and Area of a Circle
• Mathway: Circumference and Area of a Circle
• Wolfram Alpha: Circumference and Area of a Circle