Final answer:
To find the area of the circular rug, we first calculate the radius using the given circumference and then use the radius to find the area using the formula A = πr². The calculated area is approximately 7850 inches².
Step-by-step explanation:
The question asks for the approximate area of a circular rug given its circumference, using 3.14 for π (π represents the mathematical constant pi). First, we calculate the radius (r) of the circle using the circumference (πd or 2πr).
The circumference is given as 314 inches, so:
314 inches = 2 π r
r = 314 inches / (2 × π)
r = 314 inches / (2 × 3.14)
r = 50 inches
Next, we use the radius to calculate the area (A) of the circle using the formula A = πr²:
A = π × (50 inches)²
A = 3.14 × 2500 inches²
A = 7850 inches²
Therefore, the approximate area of the circular rug is 7850 inches², which corresponds to option D.