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The formula for the circurnference of a circle is \( \mathrm{C}=2 \pi \mathrm{r} \). Use this formula to wite a formula for the RADIUS of a circle. A \( r=2 \pi C \) B \( r=C-2 \pi \) C \( \mathrm{r}=\frac{c}{2 \pi} \) D \( \mathrm{r}=\frac{2 \pi}{C} \)

Ask by Wood Little. in the United States
Mar 09,2025

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Tutor-Verified Answer

Answer

The radius \( r \) is \( \frac{C}{2\pi} \).

Solution

We start with the formula for the circumference of a circle: \[ C = 2\pi r \] To solve for the radius \(r\), divide both sides of the equation by \(2\pi\): \[ r = \frac{C}{2\pi} \] Thus, the correct formula for the radius is: \[ r = \frac{C}{2\pi} \] The correct answer is option C.

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Bonus Knowledge

Did you know that the circumference formula comes from the ancient Greeks? Mathematicians like Archimedes were the first to approximate the value of pi, which is crucial in calculating circle measurements. The concept of circumference relates not just to dimensions but also to how circles appear in nature—think of tree rings, water droplets, and even the orbits of planets! When it comes to figuring out the radius, it's all about rearranging that original formula. The correct formula for the radius of a circle is \( r = \frac{C}{2\pi} \) (which is option C!). A common mistake is to forget that you need to divide by \( 2\pi \) and instead try to add or multiply, which can lead to confusion. Always remember, when it comes to equations, it’s about keeping the balance!

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