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A square park and a circular park have the same area. If the side of the square is 14 m, the radius of the circular park is approximately:
- a)6 m
- b)8 m
- c)10 m
- d)14 m
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A square park and a circular park have the same area. If the side of t...
Understanding the Problem
We have a square park and a circular park with the same area. The side of the square park is given as 14 meters. We need to find the radius of the circular park.
Calculating the Area of the Square Park
- The area of a square is calculated using the formula:
Area = side × side
- Given that the side is 14 meters:
Area of square = 14 m × 14 m = 196 m²
Setting the Area of the Circular Park
- Since the areas are equal, the area of the circular park is also 196 m².
- The formula for the area of a circle is:
Area = π × r², where r is the radius of the circle.
Finding the Radius of the Circular Park
- We set the area of the circle equal to 196 m²:
π × r² = 196
- Rearranging gives us:
r² = 196 / π
Calculating the Approximate Radius
- Using π ≈ 3.14:
r² ≈ 196 / 3.14 ≈ 62.43
- To find r, take the square root:
r ≈ √62.43 ≈ 7.9 m
Conclusion
- The radius of the circular park is approximately 8 meters.
- Therefore, the correct answer is option 'B'.
This calculation shows how to equate areas and solve for the radius of the circular park based on the given dimensions of the square park.
We have a square park and a circular park with the same area. The side of the square park is given as 14 meters. We need to find the radius of the circular park.
Calculating the Area of the Square Park
- The area of a square is calculated using the formula:
Area = side × side
- Given that the side is 14 meters:
Area of square = 14 m × 14 m = 196 m²
Setting the Area of the Circular Park
- Since the areas are equal, the area of the circular park is also 196 m².
- The formula for the area of a circle is:
Area = π × r², where r is the radius of the circle.
Finding the Radius of the Circular Park
- We set the area of the circle equal to 196 m²:
π × r² = 196
- Rearranging gives us:
r² = 196 / π
Calculating the Approximate Radius
- Using π ≈ 3.14:
r² ≈ 196 / 3.14 ≈ 62.43
- To find r, take the square root:
r ≈ √62.43 ≈ 7.9 m
Conclusion
- The radius of the circular park is approximately 8 meters.
- Therefore, the correct answer is option 'B'.
This calculation shows how to equate areas and solve for the radius of the circular park based on the given dimensions of the square park.
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Community Answer
A square park and a circular park have the same area. If the side of t...
The correct answer is Option B - 7 m
Area of the square = 142 = 196 m2.
Area of the circle = πr2.
Equating the areas gives πr2 = 196.
So r = √(196/π) = 14/√π.
Using π ≈ 3.1416, we get r ≈ 7.90 m.= 8 m
Among the given choices, the nearest value is 8 m, so the correct option is Option B.
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