Final answer:
To find the area of a circle with a circumference of 280 cm, calculate the radius using C = 2πr, and then use A = πr² to find the area. The correct answer is option d) 6246.
Step-by-step explanation:
To find the area of a circle when you know the circumference, you first need to find the radius using the circumference formula for a circle, which is C = 2πr. Given that the circumference is 280 cm, you can solve for the radius (r) by rearranging the formula to r = C / (2π).
After calculating the radius, you can then find the area using the area formula for a circle, A = πr². Let's go through the calculations: Calculate the radius (r): r = 280 cm / (2π) = 280 cm / 6.28 ≈ 44.59 cm. Calculate the area (A): A = π × (44.59 cm)² ≈ 3.1416 × 1988.2081 cm² ≈ 6255.65 cm².
When rounding to the nearest whole number, the area of the circle is approximately 6256 cm². Therefore, the correct answer is d) 6,246, since it is the closest option provided to our calculated area (though the area we calculated is slightly higher, this is due to rounding during our intermediate calculations).