Find the circumference of a circle that has an area of 452.16 square meters. (Use 3.1416 as the value of π.)

Question 1 options:

A)

24 meters

B)

75.3984 meters

C)

12 meters

D)

37.6992 meters

1 answer

To find the circumference of a circle when the area is given, we can follow these steps:

  1. Calculate the radius from the area: The area \( A \) of a circle is given by the formula: \[ A = \pi r^2 \] where \( r \) is the radius. Given the area \( A = 452.16 \) square meters and using \( \pi = 3.1416 \), we can rearrange the formula to find \( r \): \[ r^2 = \frac{A}{\pi} \] Plugging in the values: \[ r^2 = \frac{452.16}{3.1416} \approx 144 \] To find \( r \), take the square root: \[ r = \sqrt{144} = 12 , \text{meters} \]

  2. Calculate the circumference: The circumference \( C \) of a circle is given by the formula: \[ C = 2 \pi r \] Now substituting the values we have: \[ C = 2 \times 3.1416 \times 12 \] \[ C = 6.2832 \times 12 \] \[ C = 75.3984 , \text{meters} \]

Therefore, the circumference of the circle is 75.3984 meters.

The correct answer is B) 75.3984 meters.