Final answer:
The radius of a circle with an area less than 1 dm² is found using the formula A = πr². Solving the inequality πr² < 1 gives a radius less than approximately 0.5642 dm, which rounds to less than 0.56 dm.
Step-by-step explanation:
To find the radius of a circle with an area less than 1 dm², we use the formula for the area of a circle, which is A = πr². Since we know the area is less than 1 dm², we set up the inequality πr² < 1. To find the maximum radius, we divide both sides by π.
r² < 1/π
≈ r² < 0.3183
Taking the square root of both sides, we get:
r < √(0.3183)
≈ r < 0.5642 dm
Therefore, the radius of the circle is less than 0.5642 dm, which we can round down to two significant figures for precision. Hence, the radius is less than 0.56 dm.