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The circumference of a circle with radius \( r \) is given by Which of the following is the result of solving the following equation for in terms of \( C \) ?

Ask by Byrd Byrd. in the United States
Mar 11,2025

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Answer

\( r = \frac{C}{2\pi} \)

Solution

The circumference \( C \) of a circle is given by the formula: \[ C = 2\pi r \] To solve for \( r \) in terms of \( C \), we can follow these steps: 1. Start with the equation: \[ C = 2\pi r \] 2. To isolate \( r \), divide both sides of the equation by \( 2\pi \): \[ r = \frac{C}{2\pi} \] Thus, the result of solving the equation for \( r \) in terms of \( C \) is: \[ r = \frac{C}{2\pi} \]

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Beyond the Answer

The formula for the circumference \( C \) of a circle is \( C = 2\pi r \). If you want to solve this equation for \( r \) in terms of \( C \), you can rearrange the equation as follows: divide both sides by \( 2\pi \), which gives you \( r = \frac{C}{2\pi} \). It’s a neat little problem that links geometry with algebra! This equation doesn’t just work for theoretical math problems; it’s extensively used in real-life scenarios, like designing circular objects, from pizza to packaging. If you know the circumference of a wheel, you can easily calculate its radius, which is essential for ensuring proper fit and function in all sorts of mechanical applications. Isn't it great how twirling circles have such a practical touch in engineering and design?

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