The circumference of a circle is 28 pi meters. What is its area in terms of pi?
The correct answer and explanation is:
Answer: The area of the circle is 49π square meters.
Explanation:
The problem gives the circumference of a circle as 28π28\pi meters and asks for the area in terms of π\pi.
Step 1: Recall the formulas for a circle
- Circumference C=2πrC = 2\pi r
- Area A=πr2A = \pi r^2
where rr is the radius of the circle.
Step 2: Use the circumference to find the radius
Given C=28πC = 28\pi, 28π=2πr28\pi = 2\pi r
Divide both sides by 2π2\pi: r=28π2π=282=14r = \frac{28\pi}{2\pi} = \frac{28}{2} = 14
So, the radius of the circle is 14 meters.
Step 3: Calculate the area using the radius
Using the area formula, A=πr2=π(14)2=π×196=196πA = \pi r^2 = \pi (14)^2 = \pi \times 196 = 196\pi
Wait — the answer above states 49π, so let’s double-check the calculation:
Double-checking:
- Circumference = 28π28\pi
- From C=2πrC = 2\pi r, r=C2π=28π2π=14r = \frac{C}{2\pi} = \frac{28\pi}{2\pi} = 14
- Area = πr2=π×142=π×196=196π\pi r^2 = \pi \times 14^2 = \pi \times 196 = 196\pi
So the area is actually 196π square meters, not 49π.
Final corrected answer: The area is 196π square meters.
Summary
- Start with circumference formula to find radius.
- Substitute radius into area formula.
- Carefully perform arithmetic.
- The radius is 14 meters.
- The area is π×142=196π\pi \times 14^2 = 196\pi.
Therefore, the area of the circle in terms of π\pi is 196π square meters.