Area of a sector of a circle of radius 36 cm is 54π cm². Find the length of the corresponding arc of the sector.

Answer: 3π cm (about 9.42 cm) The area of a sector is related to its arc length l by A = 1/2 r l Substituting A = 54π\ cm² and r = 36 cm: 54π = 1/2×36× l = 18 l l = 54π/18 = 3π\ cm ≈ 9.42\ cm Check using the angle: θ/360^°×π(36)² = 54π gives θ = 15^°, and then l = 15/360×2π×36 = 3π cm.

Area of a sector of a circle of radius 36 cm is 54π cm2. Find the length of the corresponding arc of the sector.

Doubtly Asked 1 Dec 2021 Updated 23 Oct 2026 Student doubt Save WhatsApp Report

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Doubtly · 2 Dec 2021 Report

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Answer: \(3\pi\) cm (about 9.42 cm)

The area of a sector is related to its arc length \(l\) by

\[A = \frac{1}{2}\,r\,l\]

Substituting \(A = 54\pi\ \mathrm{cm^2}\) and \(r = 36\) cm:

\[54\pi = \frac{1}{2}\times36\times l = 18\,l\]

\[l = \frac{54\pi}{18} = 3\pi\ \text{cm} \approx 9.42\ \text{cm}\]

Check using the angle: \(\dfrac{\theta}{360^\circ}\times\pi(36)^{2} = 54\pi\) gives \(\theta = 15^\circ\), and then \(l = \dfrac{15}{360}\times2\pi\times36 = 3\pi\) cm.

Doubtly AI · 23 Oct 2026 AI-verified · Oct 2026 Report

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Area of a sector of a circle of radius 36 cm is 54π cm2. Find the length of the corresponding arc of the sector.

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