Final answer:
To find the area of the road, subtract the area of the park from the area of the larger circle.
Step-by-step explanation:
The circumference of a circle is given by the formula C=2πr, where C is the circumference and r is the radius. In this case, the circumference is given as 88 m, so we can solve for the radius: 88 = 2πr. Dividing both sides by 2π gives r = 14 m.
The width of the road surrounding the circular park is 7 m. To find the area of the road, we need to subtract the area of the park from the area of the larger circle that includes the road. The area of the park is given by the formula A=πr², so the area of the park is π(14)² = 196π m². The area of the larger circle is π(14+7)² = 441π m².
Finally, to find the area of the road, we subtract the area of the park from the area of the larger circle: 441π - 196π = 245π m².
To find the radius of the inner circle, we use the circumference formula: C = 2πr. For the park, C is 88 meters. Therefore, we solve for r: r = C / (2π) = 88 / (2π). This gives us the inner radius.
Next, we find the outer radius by adding the width of the road to the inner radius: outer radius = inner radius + 7 m.
Finally, to find the area of the road, we calculate the area of the outer circle using A = π(outer radius)^2 and subtract the area of the inner circle: inner area = π(inner radius)^2. The area of the road is then: area of road = outer area - inner area.