A circular pond of radius 4m has a path of width round it. Find the area of the path
How wide is the path?
area of a circle=22/7(r)2
radius=4m
i.e22/7(4m)2=50.3
To find the area of the path around the circular pond, we need to subtract the area of the pond itself from the area of the larger circle formed by the outer edge of the path.
The radius of the pond is 4m. Since the path is of width w, the radius of the larger circle formed by the outer edge of the path will be r = 4m + w.
The area of a circle can be calculated using the formula A = πr^2.
So, the area of the pond is A_pond = π(4^2) = 16π m^2.
The area of the larger circle, which includes the path, is A_larger_circle = π(r^2) = π((4 + w)^2) = π(16 + 8w + w^2) m^2.
Finally, the area of the path can be found by subtracting the area of the pond from the area of the larger circle: A_path = A_larger_circle - A_pond.
Substituting the values we found:
A_path = π(16 + 8w + w^2) - 16π
= 16π + 8πw + πw^2 - 16π
= 8πw + πw^2
Therefore, the area of the path is 8πw + πw^2 square meters.
To find the area of the path around 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 path.
The radius of the circular pond is given as 4m, and the width of the path is not specified, so let's assume it as 'w' meters.
The area of the pond can be calculated using the formula for the area of a circle: A = πr^2, where 'r' is the radius of the pond.
So, the area of the pond is A_pond = π(4^2) = 16π square meters.
Now, let's calculate the radius of the larger circle formed by the outer edge of the path. Since the path is formed on both sides of the pond, we need to add the radius of the pond and the width of the path to obtain the radius of the larger circle.
The radius of the larger circle is given as (4 + w) meters.
Next, we calculate the area of the path by subtracting the area of the pond from the area of the larger circle.
Area of the path = Area of the larger circle - Area of the pond
A_path = π((4 + w)^2) - 16π
Expanding the equation:
A_path = π(16 + 8w + w^2) - 16π
Now, we simplify the equation by combining like terms:
A_path = 16π + 8πw + πw^2 - 16π
Further simplifying:
A_path = 8πw + πw^2
Therefore, the area of the path is 8πw + πw^2 square meters.