CBSE Class 10 Mathematics Standard 2025: question 29

Hints

Open one hint at a time and try again before the next.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. The hour hand turns $\frac{360^{\circ }}{12}=30^{\circ }$ each hour.

   From 5 a.m. to 8 a.m. is 3 hours, so the angle swept is $\theta =3\times 30^{\circ }=90^{\circ }$.

   ½ mark

2. Area of minor sector $=\frac{\theta }{360^{\circ }}\times \pi r^2=\frac{90}{360}\times \frac{22}{7}\times (10{)}^2$

   1 mark

3. $=\frac{550}{7}{\text{ cm}}^2\approx 78.57{\text{ cm}}^2$

   ½ mark

4. Area of the whole circle $=\frac{22}{7}\times (10{)}^2=\frac{2200}{7}{\text{ cm}}^2$

   ½ mark

5. Area of major sector $=\frac{2200}{7}-\frac{550}{7}=\frac{1650}{7}{\text{ cm}}^2\approx 235.71{\text{ cm}}^2$

   ½ mark

Answer: Minor sector = 550/7 cm² ≈ 78.57 cm²; major sector = 1650/7 cm² ≈ 235.71 cm²

Revise the chapter

• Chapter: Areas Related to Circles (notes, formulas, where marks are lost and every past question)
• Topic: Area of a Sector of a Circle