A circular pond of diameter 15m is sorrounded by a path of of 2m wide find the area of the pathway
Diameter of lot = 15 m
Outside diameter of pathway = 15+2+2=19
Area of pathway+lot=π*19²/4
Area of lot only = π*15²/4
Area of pathway
= π(19²-15²)/4
= ...
106.76 square meters
To find the area of the pathway surrounding the circular pond, we need to subtract the area of the pond from the area of the larger circle formed by the outer edge of the pathway.
1. Start by finding the radius of the circular pond. The diameter is given as 15m, so the radius is half of the diameter: radius = 15m / 2 = 7.5m.
2. Next, calculate the radius of the larger circle formed by the outer edge of the pathway. Since the pathway is 2m wide on either side of the pond, the radius of the larger circle is the sum of the radius of the pond and the width of the pathway on one side. So, the radius of the larger circle is: outer radius = 7.5m + 2m = 9.5m.
3. To find the area of the pathway, we subtract the area of the circular pond from the area of the larger circle. The area of the pathway is: pathway area = π * (outer radius)^2 - π * (pond radius)^2.
- Calculate the area of the larger circle: circle area = π * (9.5m)^2.
- Calculate the area of the circular pond: pond area = π * (7.5m)^2.
- Subtract the pond area from the circle area to find the pathway area: pathway area = circle area - pond area.
4. Substitute the values into the equation and calculate the pathway area.
pathway area = π * (9.5m)^2 - π * (7.5m)^2.
5. Simplify the equation by taking out π as a common factor.
pathway area = π * [(9.5m)^2 - (7.5m)^2].
pathway area = π * [90.25m^2 - 56.25m^2].
6. Calculate the difference between the two terms inside the square brackets.
pathway area = π * 34m^2.
Therefore, the area of the pathway surrounding the circular pond is 34π square meters.