To find the radius and the area of a circle given its circumference, you can use the formulas:
1. Circumference of a circle = 2Ï€r
2. Area of a circle = πr^2
Given that the circumference of the circle is 314 cm, we can set up the equation:
2Ï€r = 314
Now, let's solve for the radius (r):
Divide both sides of the equation by 2Ï€:
r = 314 / (2Ï€)
r ≈ 314 / 6.28
r ≈ 50 cm
So, the radius of the circle is approximately 50 cm.
To find the area, we can substitute the radius into the area formula:
Area = πr^2
Area = π(50^2)
Area = π(2500)
Area ≈ 7850 cm^2
Therefore, the area of the circle is approximately 7850 cm^2.