The sides of a rectangular field are 169 m and 154 m long. Its area is equal to the area of a circular field. What is the circumference (in m) of the circular field?
Take \(\pi\) = \(\frac{22}{7}\)

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Question

This question was previously asked in

RRB NTPC Graduate Level CBT-I Official Paper (Held On: 06 Jun, 2025 Shift 1)

Answer 1

Given:

Length of rectangular field = 169 m

Breadth of rectangular field = 154 m

Area of rectangular field = Area of circular field

\(\pi = \dfrac{22}{7}\)

Formula used:

Area of rectangle = Length × Breadth

Area of circle = \(\pi r^2\)

Circumference of circle = \(2\pi r\)

Calculation:

Area of rectangle = 169 × 154

⇒ Area of rectangle = 26026 m²

Area of circle = \(\pi r^2\)

⇒ 26026 = \(\dfrac{22}{7} \times r^2\)

⇒ \(\dfrac{26026 \times 7}{22} = r^2\)

⇒ \(\dfrac{182182}{22} = r^2\)

⇒ r² = 8281

⇒ r = \(\sqrt{8281}\)

⇒ r ≈ 91 m

Circumference of circle = \(2\pi r\)

⇒ Circumference = 2 × \(\dfrac{22}{7}\) × 91

⇒ Circumference = \(\dfrac{4004}{7}\)

⇒ Circumference ≈ 572 m

∴ The correct answer is option (4).

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