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The diameter of a circular park is 17.5 m. It is surrounded by a path of width 3.5 m. The area of the path is given by
- a)220 sq. m
- b)255 sq. m
- c)231 sq. m
- d)175 sq. m
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The diameter of a circular park is 17.5 m. It is surrounded by a path ...
Option C is correct. To find the area of the path, we first need to find the area of the circular park and then subtract the area of the circular park from the area of the path.
The area of the circular park can be found using the formula:
A = π * r^2
where r is the radius of the circular park.
As we know diameter is 17.5m, radius is half of diameter, so radius of circular park is 8.75m
So,
A = π * (8.75)^2 = 231 sq. m
As we know, diameter of circular park is 17.5m, and width of the path is 3.5m.
so, total width of the path is 17.5+3.5 = 21m
so, area of the path is π*(10.5)^2 = 231 sq. m
Hence, option C is correct.
Most Upvoted Answer
The diameter of a circular park is 17.5 m. It is surrounded by a path ...
Given:
- Diameter of the circular park = 17.5 m
- Width of the path surrounding the park = 3.5 m
To Find:
- Area of the path surrounding the park
Solution:
To find the area of the path surrounding the park, we need to subtract the area of the park from the area of the larger circle formed by the outer edge of the path.
Step 1:
Find the radius of the park.
- The diameter of the park is given as 17.5 m.
- The radius of the park is half of the diameter.
- Therefore, the radius of the park = 17.5 m ÷ 2 = 8.75 m.
Step 2:
Find the radius of the larger circle formed by the outer edge of the path.
- The radius of the larger circle can be calculated by adding the radius of the park to the width of the path.
- Therefore, the radius of the larger circle = 8.75 m + 3.5 m = 12.25 m.
Step 3:
Calculate the area of the park.
- The area of a circle is given by the formula: A = πr².
- Therefore, the area of the park = π(8.75)² = 240.69 m².
Step 4:
Calculate the area of the larger circle formed by the outer edge of the path.
- The area of the larger circle = π(12.25)² = 471.24 m².
Step 5:
Calculate the area of the path surrounding the park.
- The area of the path = Area of the larger circle - Area of the park.
- Therefore, the area of the path = 471.24 m² - 240.69 m² = 230.55 m².
Answer:
The area of the path surrounding the park is 230.55 m², which is closest to option 'C' (231 sq. m).
- Diameter of the circular park = 17.5 m
- Width of the path surrounding the park = 3.5 m
To Find:
- Area of the path surrounding the park
Solution:
To find the area of the path surrounding the park, we need to subtract the area of the park from the area of the larger circle formed by the outer edge of the path.
Step 1:
Find the radius of the park.
- The diameter of the park is given as 17.5 m.
- The radius of the park is half of the diameter.
- Therefore, the radius of the park = 17.5 m ÷ 2 = 8.75 m.
Step 2:
Find the radius of the larger circle formed by the outer edge of the path.
- The radius of the larger circle can be calculated by adding the radius of the park to the width of the path.
- Therefore, the radius of the larger circle = 8.75 m + 3.5 m = 12.25 m.
Step 3:
Calculate the area of the park.
- The area of a circle is given by the formula: A = πr².
- Therefore, the area of the park = π(8.75)² = 240.69 m².
Step 4:
Calculate the area of the larger circle formed by the outer edge of the path.
- The area of the larger circle = π(12.25)² = 471.24 m².
Step 5:
Calculate the area of the path surrounding the park.
- The area of the path = Area of the larger circle - Area of the park.
- Therefore, the area of the path = 471.24 m² - 240.69 m² = 230.55 m².
Answer:
The area of the path surrounding the park is 230.55 m², which is closest to option 'C' (231 sq. m).
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The diameter of a circular park is 17.5 m. It is surrounded by a path of width 3.5 m. The area of the path is given bya)220 sq. mb)255 sq. mc)231 sq. md)175 sq. mCorrect answer is option 'C'. Can you explain this answer?
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