Question
A regular octagonal fountain has a circumradius of 10 m. Find the approximate length of each side.
This question was previously asked in
RRB NTPC 2025 Graduate CBT 2 Question Paper PDF (10-Jul-2026) (Shift 1)
The correct answer is
7.65 m
For a regular polygon with n sides and circumradius R, each side length is \(s = 2R\sin\left(\frac{180^\circ}{n}\right)\).
Here the octagon has n = 8 and R = 10 m, so \(s = 2 \times 10 \times \sin\left(\frac{180^\circ}{8}\right)\).
The angle is \(\frac{180^\circ}{8} = 22.5^\circ\), and \(\sin 22.5^\circ \approx 0.3827\).
So \(s = 20 \times 0.3827 \approx 7.65\) m.
Hence, each side of the octagonal fountain is approximately 7.65 m.
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