✓ Board-verified
Mathematics · 2025 · 2 marks
CBSE 2025 · Region 2 · Set 1 · Q22
(a) In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and ∠ AOB =90^°. If AO = OB =42 cm, then find…
In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and $\displaystyle \angle \mathrm{AOB}=90^{\circ}$. If $\displaystyle \mathrm{AO}=\mathrm{OB}=42 \mathrm{~cm}$, then find the perimeter of the top of the table.
In the given figure, three sectors of a circle of radius $\displaystyle 5$ cm, making angles $\displaystyle 35$°, $\displaystyle 50$° and $\displaystyle 95$° at the centre are shaded. Find the area of the shaded region. [Use $\displaystyle \pi=\frac{22}{7}$ ]
Marking-scheme solution
Reflex \(\displaystyle \angle \mathrm{AOB}=360^{\circ}-90^{\circ}=270^{\circ}\)
Perimeter of the top of table = length of major arc + $\displaystyle 2$ × radius
\[\begin{aligned}
& =\frac{270}{360} \times 2 \times \frac{22}{7} \times 42+2 \times 42 \\
& =282 \mathrm{~cm}
\end{aligned}
\]
Area of shaded region \(\displaystyle =\frac{95}{360} \times \frac{22}{7} \times(5)^{2}+\frac{50}{360} \times \frac{22}{7} \times(5)^{2}+\frac{35}{360} \times \frac{22}{7} \times(5)^{2}\)
\[\begin{aligned}
& =\frac{(95+50+35)}{360} \times \frac{22}{7} \times(5)^{2} \\
& =\frac{180}{360} \times \frac{22}{7} \times(5)^{2} \\
& =\frac{275}{7} \mathrm{~cm}^{2} \text { or } 39.29 \mathrm{~cm}^{2} \text { approx. }
\end{aligned}
\]
All Areas Related to Circles questions2025 question paperNCERT solutions: Areas Related to CirclesPractice Areas Related to Circles →
More from Areas Related to Circles
- An arc of a circle is of length 5 π cm and the sector it bounds has an area of 20 π cm^2. Its radius is:2025
- In the given figure, O is the centre of circle. XYZ is an arc of the circle subtending an angle of 45° at the centre. If the radius of the circle is…2026
- The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m. Find the area of the sector.2024
- 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 the clock between 5 a.m. to 8 a.m. Also,…2025
- A chord of a circle of radius 14 cm subtends an angle of 60° at the centre. Find the area of the corresponding minor segment of the circle. Also find…2023
- Anurag purchased a farmhouse which is in the form of a semicircle of diameter 70 m. He divides it into three parts by taking a point P on the…2025
- Reeti prepares a Rakhi for her brother Ronit. The Rakhi consists of a rectangle of length 8 cm and breadth 6 cm inscribed in a circle as shown in the…2023
- In the given figure, chord AB subtends an angle of 120° at the centre of the circle with radius 7 cm. Find (i) perimeter of major sector OACB, and…2026
CBSE Class 10 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.