The Circumference Of A Circle Can Be Found Using The Formula C = 2 Π R C = 2 \pi R C = 2 Π R .Which Is An Equivalent Equation Solved For R R R ?A. R = C Π R = \frac{C}{\pi} R = Π C ​ B. R = C ( 2 Π R = C(2 \pi R = C ( 2 Π ]C. R = C 2 Π R = \frac{C}{2 \pi} R = 2 Π C ​ D. $r = \frac{2

Introduction

The circumference of a circle is a fundamental concept in mathematics, and it is essential to understand the formula and its equivalent equations. 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. In this article, we will explore the equivalent equation solved for $r$ and discuss the correct answer among the given options.

Understanding the Formula

The formula $C = 2 \pi r$ is a fundamental concept in mathematics, and it is used to calculate the circumference of a circle. The circumference of a circle is the distance around the circle, and it is measured in units such as meters, feet, or inches. The radius of a circle is the distance from the center of the circle to the edge, and it is also measured in units such as meters, feet, or inches.

Solving for $r$

To solve for $r$, we need to isolate the variable $r$ on one side of the equation. We can do this by dividing both sides of the equation by $2 \pi$. This will give us the equivalent equation solved for $r$.

Equivalent Equation Solved for $r$

To find the equivalent equation solved for $r$, we need to divide both sides of the equation $C = 2 \pi r$ by $2 \pi$. This will give us:

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

Analyzing the Options

Now that we have found the equivalent equation solved for $r$, let's analyze the options given:

A. $r = \frac{C}{\pi}$

B. $r = C(2 \pi)$

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

D. $r = \frac{2}{C}$

Correct Answer

Based on our analysis, the correct answer is:

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

This is the equivalent equation solved for $r$, and it is derived from the original formula $C = 2 \pi r$ by dividing both sides by $2 \pi$.

Conclusion

In conclusion, the circumference of a circle can be found using the formula $C = 2 \pi r$. The equivalent equation solved for $r$ is $r = \frac{C}{2 \pi}$. This equation is derived from the original formula by dividing both sides by $2 \pi$. We analyzed the options given and found that option C is the correct answer.

Frequently Asked Questions

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

A: The formula for the circumference of a circle is $C = 2 \pi r$.

Q: How do I solve for $r$ in the formula $C = 2 \pi r$?

A: To solve for $r$, you need to divide both sides of the equation by $2 \pi$. This will give you the equivalent equation solved for $r$.

Q: What is the equivalent equation solved for $r$?

A: The equivalent equation solved for $r$ is $r = \frac{C}{2 \pi}$.

Q: Which option is the correct answer?

A: The correct answer is option C, $r = \frac{C}{2 \pi}$.

Final Thoughts

The circumference of a circle is a fundamental concept in mathematics, and it is essential to understand the formula and its equivalent equations. The formula $C = 2 \pi r$ is used to calculate the circumference of a circle, and the equivalent equation solved for $r$ is $r = \frac{C}{2 \pi}$. We analyzed the options given and found that option C is the correct answer.

Introduction

In our previous article, we discussed the formula for the circumference of a circle and its equivalent equations. We also analyzed the options given and found that the correct answer is $r = \frac{C}{2 \pi}$. In this article, we will provide a Q&A section to help you better understand the concept of the circumference of a circle and its equivalent equations.

Q&A Section

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

A: The formula for the circumference of a circle is $C = 2 \pi r$, where $C$ is the circumference and $r$ is the radius of the circle.

Q: What is the radius of a circle?

A: The radius of a circle is the distance from the center of the circle to the edge. It is measured in units such as meters, feet, or inches.

Q: How do I calculate the circumference of a circle?

A: To calculate the circumference of a circle, you need to use the formula $C = 2 \pi r$. Simply plug in the value of the radius and multiply it by $2 \pi$.

Q: What is the equivalent equation solved for $r$?

A: The equivalent equation solved for $r$ is $r = \frac{C}{2 \pi}$. This equation is derived from the original formula $C = 2 \pi r$ by dividing both sides by $2 \pi$.

Q: Which option is the correct answer?

A: The correct answer is option C, $r = \frac{C}{2 \pi}$.

Q: What is the significance of the value $\pi$ in the formula $C = 2 \pi r$?

A: The value $\pi$ is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14.

Q: Can I use the formula $C = 2 \pi r$ to calculate the circumference of a circle with a diameter of 10 cm?

A: Yes, you can use the formula $C = 2 \pi r$ to calculate the circumference of a circle with a diameter of 10 cm. First, you need to find the radius of the circle, which is half of the diameter. Then, you can plug in the value of the radius into the formula and multiply it by $2 \pi$.

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. As the diameter of a circle increases, its circumference also increases.

Q: Can I use the formula $C = 2 \pi r$ to calculate the circumference of a circle with a radius of 5 cm?

A: Yes, you can use the formula $C = 2 \pi r$ to calculate the circumference of a circle with a radius of 5 cm. Simply plug in the value of the radius into the formula and multiply it by $2 \pi$.

Conclusion

In conclusion, the circumference of a circle is a fundamental concept in mathematics, and it is essential to understand the formula and its equivalent equations. We provided a Q&A section to help you better understand the concept of the circumference of a circle and its equivalent equations. We hope this article has been helpful in clarifying any doubts you may have had.

Frequently Asked Questions

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

A: The formula for the circumference of a circle is $C = 2 \pi r$.

Q: How do I calculate the circumference of a circle?

A: To calculate the circumference of a circle, you need to use the formula $C = 2 \pi r$. Simply plug in the value of the radius and multiply it by $2 \pi$.

Q: What is the equivalent equation solved for $r$?

A: The equivalent equation solved for $r$ is $r = \frac{C}{2 \pi}$.

Q: Which option is the correct answer?

A: The correct answer is option C, $r = \frac{C}{2 \pi}$.

Final Thoughts

The circumference of a circle is a fundamental concept in mathematics, and it is essential to understand the formula and its equivalent equations. We hope this article has been helpful in clarifying any doubts you may have had. If you have any further questions or concerns, please feel free to ask.