Questions: Find the circumference of a circle if the area is 300 square centimeters. A) 61.38 cm B) 56.25 cm C) 84.74 cm D) 9.77 cm

Solution Steps

To find the circumference of a circle given its area, we can use the following steps:

1. Use the formula for the area of a circle, \( A = \pi r^2 \), to solve for the radius \( r \).
2. Once the radius is found, use the formula for the circumference of a circle, \( C = 2 \pi r \), to find the circumference.

Given the area of the circle \( A = 300 \) square centimeters, we use the formula for the area of a circle: \[ A = \pi r^2 \] Solving for the radius \( r \): \[ r = \sqrt{\frac{A}{\pi}} = \sqrt{\frac{300}{\pi}} \approx 9.772 \text{ cm} \]

Using the radius \( r \approx 9.772 \) cm, we can find the circumference \( C \) using the formula: \[ C = 2 \pi r \] Substituting the value of \( r \): \[ C = 2 \pi \times 9.772 \approx 61.40 \text{ cm} \]

Final Answer