Question

""Find the exact area of a circle having the given circumference:

Circumference = 3π

Area = ?

1. 2.25π
2. 9π
3. 3π""

Please select the correct option for the area of the circle.

Answer 1

The exact area of a circle with a circumference of 3π is 2.25π square units, by first finding the radius to be 1.5 and then using the area formula.

Step-by-step explanation:

To find the exact area of a circle with a given circumference, we use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius of the circle. Given the circumference is 3π, we solve for r by rearranging the formula to r = C / (2π). Substituting the given value, we have r = 3π / (2π) = 1.5.

Now, to find the area A, we use the formula A = πr², substituting our value for the radius, we have A = π(1.5)² = π(2.25) = 2.25π. Therefore, the area of the circle is 2.25π square units, which corresponds to option 1.