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Mathematics · 2026 · 3 marks
CBSE 2026 · Region 4 · Set 2 · Q31
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.
The perimeter of sector OAB of a circle with centre O and radius $\displaystyle 5.6$ cm , is $\displaystyle 15.6$ cm. Find length of the arc AB. Also find the value of $\displaystyle \theta$.
Marking-scheme solution
Length of the arc AB = Perimeter of sector - 2r
\[\text { = } 15.6 \text { - } 11.2
\]
\[=4.4 \mathrm{~cm}
\]
\[\begin{aligned}
& \therefore 4.4=\frac{\theta}{360} \times 2 \times \frac{22}{7} \times 5.6 \\
& \Rightarrow \theta=45^{0}
\end{aligned}
\]
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