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The circular grass lawn of radius 35 m has a path of width 7 m around it on the outside. What is the area of the path?
- a)1496m2
- b)1450m2
- c)1576m2
- d)1694m2
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The circular grass lawn of radius35m has a path of width7maround it on...
Understanding the Problem
To find the area of the path around the circular lawn, we first need to determine the dimensions of both the lawn and the path.
Dimensions of the Lawn and Path
- Radius of the lawn: 35 m
- Width of the path: 7 m
- Total radius (lawn + path): 35 m + 7 m = 42 m
Calculating Areas
1. Area of the lawn:
- Formula: Area = π * radius^2
- Area of the lawn = π * (35 m)^2
2. Area of the larger circle (lawn + path):
- Area of the larger circle = π * (42 m)^2
Finding the Area of the Path
- Area of the path: This is the area of the larger circle minus the area of the lawn.
- Area of the path = Area of the larger circle - Area of the lawn
Calculating the Values
- Area of the lawn = π * 1225 = 1225π m²
- Area of the larger circle = π * 1764 = 1764π m²
- Area of the path = 1764π - 1225π = (1764 - 1225)π = 539π m²
Final Calculation
Using the approximate value of π (3.14):
- Area of the path = 539 * 3.14 ≈ 1694.06 m²
Thus, the area of the path is approximately 1694 m², confirming that the correct answer is option D.
To find the area of the path around the circular lawn, we first need to determine the dimensions of both the lawn and the path.
Dimensions of the Lawn and Path
- Radius of the lawn: 35 m
- Width of the path: 7 m
- Total radius (lawn + path): 35 m + 7 m = 42 m
Calculating Areas
1. Area of the lawn:
- Formula: Area = π * radius^2
- Area of the lawn = π * (35 m)^2
2. Area of the larger circle (lawn + path):
- Area of the larger circle = π * (42 m)^2
Finding the Area of the Path
- Area of the path: This is the area of the larger circle minus the area of the lawn.
- Area of the path = Area of the larger circle - Area of the lawn
Calculating the Values
- Area of the lawn = π * 1225 = 1225π m²
- Area of the larger circle = π * 1764 = 1764π m²
- Area of the path = 1764π - 1225π = (1764 - 1225)π = 539π m²
Final Calculation
Using the approximate value of π (3.14):
- Area of the path = 539 * 3.14 ≈ 1694.06 m²
Thus, the area of the path is approximately 1694 m², confirming that the correct answer is option D.
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Community Answer
The circular grass lawn of radius35m has a path of width7maround it on...
r = 35 m; R = 35+7=42 m
Formula for area of a circle:
Area = πr²
Area of inner circle:
Area = 22/7 × 35²
35² = 1225
Area = 22/7 × 1225 = 22 × 175 = 3850 m²
Area of outer circle:
Area = 22/7 × 42²
42² = 1764
Area = 22/7 × 1764 = 22 × 252 = 5544 m²
Area of path = Area of outer circle -Area of inner circle
Area of path = 5544 − 3850 = 1694m2
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The circular grass lawn of radius35m has a path of width7maround it on the outside. What is the area of the path?a)1496m2b)1450m2c)1576m2d)1694m2Correct answer is option 'D'. Can you explain this answer?
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