CBSE 2025 · Region 2 · Set 1 · Q22 · 2 marks
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 $\displaystyle \pi=\frac{22}{7}$ ]
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 \(\displaystyle =\frac{95}{360} \times \frac{22}{7} \times(5)^{2}+\frac{50}{360} \times \frac{22}{7} \times(5)^{2}+\frac{35}{360} \times \frac{22}{7} \times(5)^{2}\)
\[\begin{aligned}
& =\frac{(95+50+35)}{360} \times \frac{22}{7} \times(5)^{2} \\
& =\frac{180}{360} \times \frac{22}{7} \times(5)^{2} \\
& =\frac{275}{7} \mathrm{~cm}^{2} \text { or } 39.29 \mathrm{~cm}^{2} \text { approx. }
\end{aligned}
\]
Areas Related to CirclesArea of a Sector of a CircleApplyvery_short_answermedium
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CBSE Class 10 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.