There is a circular park in front of a shopping mall whose radius is 20 cm. There is a gravel path of uniform width of 2m around the park. What is the area of the gravelled path?
A park with a radius of 20 cm? That means that a person's footprint is larger than the circular park.
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To find the area of the gravel path around the circular park, we need to subtract the area of the park from the area of the larger circle that includes the path.
1. Find the area of the circular park:
The area of a circle is given by the formula A = π * r^2, where A is the area and r is the radius.
In this case, the radius of the park is 20 cm, so the area of the park is A_park = π * (20 cm)^2.
2. Find the radius of the larger circle:
Since the path around the park has a uniform width of 2m, the radius of the larger circle will be the sum of the radius of the park and the width of the path.
Convert the width of the path from meters to centimeters: 2m = 200 cm.
The radius of the larger circle is then r_larger = 20 cm + 200 cm.
3. Find the area of the larger circle:
Using the formula A = π * r^2, where A is the area and r is the radius, the area of the larger circle is A_larger = π * (r_larger)^2.
4. Find the area of the gravelled path:
The area of the gravelled path is the difference between the area of the larger circle and the area of the park.
Area_of_path = A_larger - A_park.
Now, you can calculate the area of the gravelled path using the given information and the steps outlined above.