Answer:
2. The area of the side walk is approximately 217 m²
3. The distance away from the sprinkler the water can spread is approximately 11 feet
4. The area of the rug is 49.6
Explanation:
2. The dimensions of the flower bed and the sidewalks are;
The diameter of the flower bed = 20 meters
The width of the circular side walk, x = 3 meters
Therefore, the diameter of the outer edge of the side walk, D, is given as follows
D = d + 2·x (The width of the side walk is applied to both side of the circular diameter)
∴ D = 20 + 2×3 = 26
The area of the side walk = The area of the sidewalk and the side walk = The area of the flower bed
∴ The area of the side walk, A = π·D²/4 - π·d²/4
∴ A = 3.14 × 26²/4 - 3.14 × 20²/4 = 216.66
By rounding to the nearest whole number, the area of the side walk, A ≈ 217 m²
3. Given that the area formed by the circular pattern, A = 379.94 ft.², we have;
Area of a circle = π·r²
∴ Where 'r' represents how far it can spread, we have;
π·r² = 379.94
r = √(379.94 ft.²/π) ≈ 10.997211 ft.
Therefore, the distance away from the sprinkler the water can spread, r ≈ 11 feet
4. The circumference of the rug = 24.8 meters
The circumference of a circle, C = 2·π·r
Where;
r = The radius of the circle
π = 3.1
∴ For the rug of radius 'r', C = 2·π·r = 24.8
r = 24.8/(2·π) = 12.4/π = 12.4/3.1 = 4
The area = π·r²
∴ The area of the rug = 3.1 × 4² = 49.6.