A pond 100 ft in diameter is surrounded by a circular grass walk 2 feet wide. Find the are of the walk. Answer in terms of π.
Please help me! TY
area of pond = π(50)^2 = 2500π
area of pond plus walkway = π(52)^2 = 2704π
area of walkway = 2704π-2500π = 204π
To find the area of the grass walk, we need to subtract the area of the pond from the area of the larger circle that encompasses both the pond and the grass walk.
1. Calculate the area of the larger circle:
The diameter of the larger circle is the sum of the diameter of the pond (100 ft) and twice the width of the grass walk (2 ft × 2 = 4 ft).
So, the diameter of the larger circle is 100 ft + 4 ft = 104 ft.
The radius of the larger circle is half of its diameter, so 104 ft ÷ 2 = 52 ft.
The area of the larger circle is A = πr², where r is the radius.
Thus, the area of the larger circle is A = π(52 ft)².
2. Calculate the area of the pond:
The diameter of the pond is given as 100 ft, so its radius is half of its diameter, which is 100 ft ÷ 2 = 50 ft.
The area of the pond is A = πr², where r is the radius.
Thus, the area of the pond is A = π(50 ft)².
3. Subtract the area of the pond from the area of the larger circle:
The area of the grass walk is the difference between the areas of the larger circle and the pond.
So, the area of the grass walk is π(52 ft)² - π(50 ft)², which simplifies to π((52 ft)² - (50 ft)²).
Hence, the area of the grass walk is π((52 ft)² - (50 ft)²).