A circular park of radius 20m is situated in a colony

General
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a circular park of radius 20m is situated in a colony

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Circular Park in a Colony

Answer:

The subject of the conversation revolves around a circular park with a radius of 20 meters situated within a colony. This scenario encompasses several mathematical and practical elements that can be explored further.

Step 1: Basic Geometric Properties

Understanding the basic geometric properties of a circular park is essential.

  • Radius: 20 meters

  • Diameter: The diameter of the circle is twice the radius, so it’s 40 meters.

  • Circumference: The circumference of a circle can be calculated using the formula C = 2\pi r, where (C) is the circumference and (r) is the radius.

    C = 2 \pi \times 20 = 40 \pi \text{ meters}

    Approximating (\pi) as 3.14, the circumference is roughly 125.6 meters.

  • Area: The area of a circle is found using the formula A = \pi r^2, where (A) is the area and (r) is the radius.

    A = \pi \times (20)^2 = 400 \pi \text{ square meters}

    Again, using (\pi) ≈ 3.14, the area approximates to 1256 square meters.

Step 2: Practical Implications and Uses

Discussing the placement of such a park within a colony provides various insights and applications:

  • Community Design: Such parks generally serve as recreational spaces, play areas, and community gathering points.
  • Environmental Impact: A park can positively affect the environment by improving air quality, offering green space, and providing habitat for local wildlife.
  • Urban Planning Considerations: When planning a circular park, important factors include accessibility, integration with existing infrastructure, and the needs of the community.

Step 3: Additional Mathematical Exploration

Considering additional explorations:

  • Perimeter Path: Designing a walking or jogging path along the perimeter of the park provides an excellent exercise area. Given the circumference, this path measures approximately 125.6 meters.

  • Segment and Sector Analysis: For advanced mathematics, analyzing segments and sectors within the circle can be conducted. This includes finding segment areas using calculus or determining arc lengths for specific angles.

Final Answer:

A circular park in a colony with a radius of 20 meters encompasses not only geometric characteristics such as having a diameter of 40 meters, a circumference of about 125.6 meters, and an area of approximately 1256 square meters, but also involves community, environmental, and urban planning implications. Mathematical explorations can extend to the design of peripheral paths and the analysis of specific segments and sectors within the circle.