Final answer:
To find the radius, divide the circumference by 2π. To find the area, plug the radius into the area formula πr².
Step-by-step explanation:
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. To find the radius (r), you can rearrange the formula to r = C / (2π). Given that the circumference is 31.4 cm and π (pi) is approximately 3.14, we calculate the radius as follows:
Circumference = 2πr
Area = πr²
Given that the circumference of the circle is 31.4 cm, we can plug in this value to the circumference formula and solve for the radius:
31.4 = 2πr
r = 31.4 / (2π) ≈ 5 cm
Now, we can use the radius we found to calculate the area of the circle:
Area = π(5)² = 25π ≈ 78.5 cm²