1. The problem states that the area of a circle is 46.3 cm² and asks us to find its radius, using \(\pi = 3.14\). We need to round the answer to 2 significant digits. 2. Recall the formula for the area of a circle: $$ A = \pi r^2 $$ where \(A\) is the area and \(r\) is the radius. 3. Substitute the given values into the formula: $$ 46.3 = 3.14 \times r^2 $$ 4. Solve for \(r^2\): $$ r^2 = \frac{46.3}{3.14} $$ Calculate: $$ r^2 \approx 14.75 $$ 5. Take the square root of both sides to find \(r\): $$ r = \sqrt{14.75} $$ Calculate: $$ r \approx 3.84 $$ 6. Round \(r\) to 2 significant digits: $$ r \approx 3.8 $$ 7. Therefore, the radius of the circle is approximately \(3.8\) cm. Answer: 3.8