The radius of the circle is approximately 4.9 cm, and the area is approximately 78.46 square centimeters.
We can find the radius and area of the circle using the given information and the following formulas:
Circumference: C = 2πr
Area: A = πr²
where:
C is the circumference
A is the area
r is the radius
π (pi) is a mathematical constant approximately equal to 3.14
Step 1: Solve for the radius (r)
We know the circumference (C) is 31.4 cm and pi (π) is 3.14. We can rearrange the formula for circumference to solve for r:
r = C / (2π)
Substituting the known values:
r = 31.4 cm / (2 * 3.14)
r ≈ 4.9975 cm
Therefore, the radius of the circle is approximately 4.9975 centimeters.
Step 2: Calculate the area (A)
Now that we know the radius, we can use the formula for area:
A = πr²
Substituting the known value of r:
A = 3.14 * (4.9975 cm)²
A ≈ 78.46 cm²
Therefore, the area of the circle is approximately 78.46 square centimeters.
Question
The circumference of a circle is 31.4cm. Find the radius and area of the circle.[Take pi=3.14]