Final answer:
To find the cost of paving a path around a circular park, calculate the area of the outer circle and inner circle using the formula A = πr², subtract the inner area from the outer area to get the area of the path, and then multiply by the cost per square meter.
Step-by-step explanation:
The question asks us to calculate the cost of paving a path around a circular park. The diameter of the park is given as 24 meters, which means the radius of the park is 12 meters (half of the diameter). The path is 3 meters wide, which means we have an outer circle (the edge of the path) with a radius of 12 meters, and an inner circle (the edge of the park) with a radius of 12 meters - 3 meters = 9 meters.
To find the area of the path, we need to calculate the area of the outer circle and subtract the area of the inner circle from it.
The formula to calculate the area of a circle is A = πr². Thus, the area of the outer circle (A_outer) is π(12m)² and the area of the inner circle (A_inner) is π(9m)². Subtracting the inner area from the outer area gives us the area of the path:
A_path = A_outer - A_inner.
After calculating the area of the path, the last step is to multiply the area of the path by the paving cost per square meter, which is given as 25 per square meter. So the final cost will be the area of the path multiplied by 25.