Mathematics

A rectangular park has dimensions 240 m by 200 m. A circular lawn is made inside the park. If the area of the park excluding the lawn is 32600 sq m, find the circumference of the lawn.

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Given: Dimensions of the rectangular park = 240 m × 200 m

Area of the park excluding the lawn = 32,600 m²

Area of the rectangular park = 240 × 200 = 48,000 m²

Area of lawn = Total area of park − Area excluding lawn = 48,000 − 32,600 = 15,400 m²

Area of a circle = 𝜋𝑟²

⇒ 𝜋𝑟² = 15,400

⇒ 𝑟² = $\dfrac{15,400}{𝜋}$

Using 𝜋 ≈ 3.1416

⇒ 𝑟² = $\dfrac{15,400}{3.1416}$

⇒ r ≈ $\sqrt{4,905.63}$

⇒ 𝑟 ≈ 70.03 m

Circumference of the lawn = 2𝜋𝑟 = 2 × 3.1416 × 70.03 ≈ 440 m

Hence, the circumference of the lawn = 440 m.

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