Final answer:
To find the circumference of a circle with an area of 100π m², we first determine the radius by taking the square root of the area divided by pi, yielding 10 m. We then use the circumference formula 2πr, resulting in a circumference of 20π m.
Step-by-step explanation:
The area of a circle is given by the formula A = πr², indicating the area A is pi times the radius squared. When given that the area of a circle is 100π m², we can find the radius of the circle by taking the square root of the area divided by pi, which would give us r = √(100π/π) = 10 m.
Once we have the radius, we can find the circumference using the formula C = 2πr. Substituting the radius we found, the circumference C will be 2π*10 m, which simplifies to 20π m.