Find the area of a circle in terms of π if the diameter is 6. A. 3π B. 6π C. 9π D. 36π E. None of the above
The Correct Answer and Explanation is:
The formula for the area of a circle is:A=πr2A = \pi r^2A=πr2
where AAA is the area and rrr is the radius of the circle.
We are given the diameter of the circle, which is 6. The radius rrr is half of the diameter, so:r=62=3r = \frac{6}{2} = 3r=26=3
Now, using the formula for the area of a circle, we substitute the value of rrr:A=π(3)2=π×9=9πA = \pi (3)^2 = \pi \times 9 = 9\piA=π(3)2=π×9=9π
Thus, the area of the circle is 9π9\pi9π.
Conclusion:
The correct answer is C. 9π.
Explanation:
- The area of any circle is found using the formula A=πr2A = \pi r^2A=πr2.
- The diameter is 6, so the radius is 3.
- Squaring the radius (3) gives 9, and multiplying by π\piπ results in 9π9\pi9π.
- Therefore, the area of the circle is 9π9\pi9π, which corresponds to option C.
