The area of a circle is 100pi in^2 . What is the circumference , in inches?Express your answer in terms of pi Answer Attempt 2 out of 2 C=square in Submit Answer

To find the circumference of a circle given its area, we can use the following steps:<br /><br />1. **Recall the formula for the area of a circle:**<br /> \[<br /> A = \pi r^2<br /> \]<br /> where \( A \) is the area and \( r \) is the radius.<br /><br />2. **Given the area \( A = 100\pi \) square inches, we can set up the equation:**<br /> \[<br /> \pi r^2 = 100\pi<br /> \]<br /><br />3. **Divide both sides of the equation by \( \pi \) to isolate \( r^2 \):**<br /> \[<br /> r^2 = 100<br /> \]<br /><br />4. **Take the square root of both sides to solve for \( r \):**<br /> \[<br /> r = \sqrt{100} = 10 \text{ inches}<br /> \]<br /><br />5. **Now, use the formula for the circumference of a circle:**<br /> \[<br /> C = 2\pi r<br /> \]<br /><br />6. **Substitute \( r = 10 \) inches into the circumference formula:**<br /> \[<br /> C = 2\pi \times 10 = 20\pi \text{ inches}<br /> \]<br /><br />Therefore, the circumference of the circle is:<br />\[<br />C = 20\pi \text{ inches}<br />\]<br /><br />So, the final answer is:<br />\[<br />C = 20\pi \text{ in}<br />\]