✓ Board-verified
Mathematics · 2024 · 5 marks
CBSE 2024 · Region 1 · Set 3 · Q35
In the given figure, diameters AC and BD of the circle intersect at O . If $\displaystyle \angle \mathrm{AOB}=60^{\circ}$ and $\displaystyle \mathrm{OA}=10 \mathrm{~cm}$, then :(i)find the length of the chord AB.(ii)find the area of shaded region. (Take $\displaystyle \pi=3.14$ and $\displaystyle \sqrt{3}=1.73$ )
In the given figure, diameters AC and BD of the circle intersect at O . If $\displaystyle \angle \mathrm{AOB}=60^{\circ}$ and $\displaystyle \mathrm{OA}=10 \mathrm{~cm}$, then :
(i)
find the length of the chord AB.
(ii)
find the area of shaded region. (Take $\displaystyle \pi=3.14$ and $\displaystyle \sqrt{3}=1.73$ )
Marking-scheme solution
(i)
\(\displaystyle \Delta \mathrm{OAB}\) is an equilateral triangle.
\[\therefore \mathrm{AB}=\mathrm{OA}=10 \mathrm{~cm}
\]
(ii)
Area of segment APB \(\displaystyle \left(\mathrm{A}_{1}\right)=3.14 \times 100 \times \frac{60}{360}-\frac{1.73}{4} \times 100\)
\[=9.08 \mathrm{~cm}^{2} \text { approx. }
\]
\[\begin{aligned}
\text { Area of sector } \mathrm{OBC}\left(\mathrm{~A}_{2}\right) & =3.14 \times 100 \times \frac{120}{360} \\
& =104.67 \mathrm{~cm}^{2} \text { approx. }
\end{aligned}
\]
\[\text { Area of shaded region }=\mathrm{A}_{1}+\mathrm{A}_{2}=113.75 \mathrm{~cm}^{2} \text { approx. }
\]
More from Areas Related to Circles
- The length of the hour hand of a clock is 10 cm. Find the area of the minor sector swept by the hour hand of…2025 · asked 3×
- A chord of a circle of radius 14 cm subtends an angle of 60° at the centre. Find the area of the…2023 · asked 3×
- Anurag purchased a farmhouse which is in the form of a semicircle of diameter 70 m. He divides it into three…2025 · asked 3×
- In the given figure, chord AB subtends an angle of 120° at the centre of the circle with radius 7 cm. Find…2026 · asked 3×
- The perimeter of the sector of a circle of radius 21 cm which subtends an angle of 60° at the centre of…2024 · asked 3×
- In Fig. 1, there are two concentric circles with centre O. If ARC and AQB are tangents to the smaller circle…2022 · asked 3×
- A piece of wire 20 cm long is bent into the form of an arc of a circle of radius 60/(π) cm. The angle…2025 · asked 3×
- The circumferences of two circles are in the ratio 4: 5. What is the ratio of their radii?2023 · asked 3×
CBSE Class 10 Mathematics past-paper question from the 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.