Case Study Questions on Areas Related to Circles Class 10

Case Study Questions on Areas Related to Circles Class 10 | Maths Case Studies

Introduction to Circle-Based Case Studies

In Class 10 mathematics, students often solve Case Study Questions on Areas Related to Circles Class 10. These problems combine theory with real-life examples such as calculating shaded regions, arcs, and segments. Through Case Study Class 10 Maths Areas Related to Circles, learners strengthen their ability to apply formulas effectively.

Importance of Circle Case Study Questions

Practicing Class 10 Areas Related to Circles Case Study Questions builds confidence. They help in understanding concepts like the area of a sector, segment, and ring-shaped figures. Moreover, Cbse Class 10 Case Study Questions on Circles improve analytical thinking and prepare students for board exams. Therefore, these problems are crucial for scoring well.

Preparation Tips for Success

When solving Case Study Questions Maths Class 10 Areas Related to Circles, students should revise formulas regularly. Additionally, referring to Ncert Case Study Questions Class 10 Maths Circles ensures concept clarity. Solved Areas Related to Circles Case Study Class 10 examples also help reduce errors. Finally, consistent practice improves both speed and accuracy.

Case Study 1: Circular Park with Fountain and Benches

Case Study 1

A circular park in a town is surrounded by a walking track. The radius of the park is 35 m. A fountain is constructed at the center, covering a circular region of radius 7 m. The remaining space is covered with grass. The municipality decides to build two benches along the boundary of the fountain, each covering a sector of the circular region. The angle of each sector is $90^{\circ}$. The rest of the grass area is left open for visitors. Students of a nearby school are asked to calculate the areas of different parts for a project.

MCQ Questions:

1. What is the area of the circular park?

  • (a) $3850 \ \text{m}^2$
  • (b) $3850 \pi \ \text{m}^2$
  • (c) $3848 \ \text{m}^2$
  • (d) $3849 \ \text{m}^2$
Answer: (b) $3850 \pi \ \text{m}^2$
Solution: Area of circle $= \pi r^2 = \pi (35)^2 = 1225 \pi = 3850 \pi \ \text{m}^2$.

2. What is the area covered by the fountain?

  • (a) $49 \pi \ \text{m}^2$
  • (b) $154 \pi \ \text{m}^2$
  • (c) $300 \ \text{m}^2$
  • (d) $150 \ \text{m}^2$
Answer: (b) $154 \pi \ \text{m}^2$
Solution: Area $= \pi (7)^2 = 49 \pi \ \text{m}^2 = 154 \pi \ \text{m}^2$.

3. What is the area of the grass-covered region?

  • (a) $3696 \pi \ \text{m}^2$
  • (b) $3800 \pi \ \text{m}^2$
  • (c) $3848 \pi \ \text{m}^2$
  • (d) $3700 \pi \ \text{m}^2$
Answer: (a) $3696 \pi \ \text{m}^2$
Solution: Grass area $= 3850 \pi – 154 \pi = 3696 \pi \ \text{m}^2$.

4. Each bench covers a $90^\circ$ sector of the fountain. What is the total area of the two benches?

  • (a) $77 \pi \ \text{m}^2$
  • (b) $98 \pi \ \text{m}^2$
  • (c) $154 \pi \ \text{m}^2$
  • (d) $100 \ \pi \ \text{m}^2$
Answer: (a) $77 \pi \ \text{m}^2$
Solution: Area of one $90^\circ$ sector $= \dfrac{90}{360} \times 154 \pi = 38.5 \pi$.
For two benches $= 2 \times 38.5 \pi = 77 \pi \ \text{m}^2$.
Correction: Correct calculation: $ \dfrac{90}{360} \times 154 \pi = 38.5 \pi$. For 2 benches = $77 \pi \ \text{m}^2$. Hence correct option is (a), not (b).

5. What is the remaining grass area after placing the benches?

  • (a) $3619 \pi \ \text{m}^2$
  • (b) $3615 \pi \ \text{m}^2$
  • (c) $3620 \pi \ \text{m}^2$
  • (d) $3600 \pi \ \text{m}^2$
Answer: (a) $3619 \pi \ \text{m}^2$
Solution: Remaining grass $= 3696 \pi – 77 \pi = 3619 \pi \ \text{m}^2$.

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