A park is in the form of a rectangle 100 m×80 mat. At the centre of the park there is a circular lawn. The area of the park excluding the lawn is 4150 m^2 find the radius of the circular lawn
100 * 80 = 8,000 sq. m.
8,000 - 4150 = 3,850 sq. m.
A = pi * r^2
3,850 = 3.14 * r^2
1,226.11 = r^2
? = r
To find the radius of the circular lawn, we need to subtract the area of the circle from the total area of the park.
Step 1: Calculate the area of the park.
Given that the park is a rectangular shape with dimensions 100m x 80m, we can calculate its area using the formula:
Area = Length x Width
Area = 100m x 80m
Area = 8000m^2
Step 2: Subtract the area of the lawn from the total park area to find the remaining area.
Given that the area excluding the lawn is 4150m^2, we subtract this area from the total park area:
Remaining Area = Total Area - Lawn Area
Remaining Area = 8000m^2 - 4150m^2
Remaining Area = 3850m^2
Step 3: Calculate the radius of the circular lawn using the remaining area.
We know that the area of a circle is given by the formula:
Area of a Circle = π * r^2
where π is a constant approximately equal to 3.14, and r is the radius of the circle.
So, we can rearrange this formula to solve for the radius:
r = sqrt(Area of Circle / π)
Plugging in the remaining area, we can find the radius:
r = sqrt(3850m^2 / 3.14)
r ≈ sqrt(1226.75m^2)
r ≈ 35m
Therefore, the radius of the circular lawn is approximately 35 meters.