Questions: Find the circumference of a circle that has an area of 452.16 square meters. (Use 3.1416 as the value of π.) A) 12 meters B) 24 meters C) 75.3984 meters D) 37.6992 meters

Solution Steps

To find the circumference of a circle given its area, we first need to determine the radius. The area \( A \) of a circle is given by the formula \( A = \pi r^2 \). We can solve for the radius \( r \) by rearranging this formula. Once we have the radius, we can find the circumference \( C \) using the formula \( C = 2\pi r \).

Given the area \( A = 452.16 \, \text{m}^2 \) and using the formula for the area of a circle \( A = \pi r^2 \), we can solve for the radius \( r \):

\[ r = \sqrt{\frac{A}{\pi}} = \sqrt{\frac{452.16}{3.1416}} \approx 11.9969 \, \text{m} \]

Now that we have the radius, we can find the circumference \( C \) using the formula \( C = 2\pi r \):

\[ C = 2 \times 3.1416 \times 11.9969 \approx 75.3792 \, \text{m} \]

Final Answer