Q) The perimeter of sector OAB of a circle with centre O and radius 5.6 cm, is 15.6 cm. Find length of the arc AB. Also find the value of θ.

(Q 31 – 30/4/2 – CBSE 2026 Question Paper)

Ans:

Length of Arc AB:

We are given: Perimeter of sector OAB = 15.6 cm

Length of radius OA & OB = 5.6 cm

∵ The perimeter of sector OAB is given by = length of Arc AB + OA + OB

∴ 15.6 = Arc AB + 2 (5.6)

∴ Arc AB = 15.6 – 11.2 = 4.4

Therefore, length of Arc AB is 4.4 cm

Value of θ: 

Since length of Arc is given by: 2 π r

Here, length of arc AB = 4.4 cm (calculated above)

Radius r = 5.6 cm

∴ for length of the arc AB:

2 (5.6) = 4.4

∴ 44 (0.8) = 4.4

∴ =

∴ =

∴ θ = = 45 ⁰

Therefore, the value of θ is 45 ⁰

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