Olivia is told that the circumference of a circle is equal to 8pi How can she use this value to calculate the area of the circle without first, finding the radius of the circle?
To calculate the area of a circle using the circumference, Olivia can use the formula:
A = (C²) / (4π)
where A is the area and C is the circumference.
Given that the circumference is 8π, Olivia can substitute this value into the formula to determine the area:
A = ((8π)²) / (4π)
Simplifying the expression inside the brackets, we have:
A = (64π²) / (4π)
The π in the numerator and denominator cancels out, leaving:
A = 16π
Therefore, the area of the circle is 16π.