Short Answer 
To find the radius of a circle with an area less than 1 dm¬≤, we use the area formula A = œAr¬≤ and set up the inequality œAr¬≤ < 1. By rearranging, we find r¬≤ < 1/œA, leading to a maximum radius of approximately 0.5642 dm, which rounds to less than 0.56 dm.
Step 1: Use the Area Formula
To determine the radius of a circle with an area less than 1 dm¬¨‚â§, we begin by applying the area formula for a circle, which is A = ≈ìAr¬¨‚â§. Here, A represents the area, while r is the radius. Since we’re focused on an area less than 1 dm¬¨‚â§, we set up the inequality by writing it as ≈ìAr¬¨‚⧠< 1.
Step 2: Rearranging the Inequality
Next, we need to isolate the variable r in our inequality. We achieve this by dividing both sides of the inequality by œA. This simplifies our expression to r¬≤ < 1/œA, which further calculates to approximately 0.3183. The goal here is to express the inequality in a form that can easily lead us to the value of the radius.
Step 3: Calculate the Radius
Finally, we find the radius by taking the square root of both sides of the adjusted inequality. This results in r < ‚Äöao(0.3183), which simplifies to approximately 0.5642 dm. For clarity and precision, we round this value to less than 0.56 dm, indicating the maximum possible radius of the circle under the given area constraint.