Class 10 Math Areas Related to Circles MCQ Test

Class 10 Math Areas Related to Circles MCQ Test: Enhance your understanding with free online multiple-choice questions for CBSE Class 10 Math Chapter 11. Master the concepts of areas of circles, sectors, and segments. Ideal for CBSE exam preparation and competitive tests.

Areas Related to Circles MCQ Test Quiz

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10th Math: Areas Related to Circles

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About Areas Related to Circles

Chapter 11 of the CBSE Class 10 Math curriculum, titled “Areas Related to Circles,” focuses on calculating and understanding various areas associated with circles. This chapter covers the areas of circles, sectors, and segments, and includes important formulas and applications. The free MCQ quiz provided in this chapter will help students solidify their understanding and prepare effectively for their CBSE examinations.

Key Concepts Covered:

Area of a Circle:
- Formula: The area
  
  $A$ of a circle with radius
  
  $r$ is given by: $\pi r^2$
  
  $A = π r^{2}$
- Application: Used to calculate the surface area of circular objects and regions.
Circumference of a Circle:
- Formula: The circumference
  
  $C$ of a circle with radius
  
  $r$ is given by: $\pi r$
  
  $C = 2 π r$
- Application: Used to determine the boundary length of circular objects.
Sector of a Circle:
- Definition: A sector is a portion of a circle enclosed by two radii and the arc between them.
- Area of Sector: The area $AsectorA_{\text{sector}}$
  
  $A_{sector}$ of a sector with radius
  
  $r$ and angle $θ\theta$
  
  $θ$ (in degrees) is: $Asector=θ360∘⋅πr2A_{\text{sector}} = \frac{\theta}{360^\circ} \cdot \pi r^2$
  
  $A_{sector} = 360 ^{\circ} θ \cdot π r^{2}$
- Length of Arc: The length
  
  $L$ of the arc of a sector with radius
  
  $r$ and angle $θ\theta$
  
  $θ$ (in degrees) is: $\frac{\theta}{360^\circ} \cdot 2 \pi r$
  
  $L = 360 ^{\circ} θ \cdot 2 π r$
Segment of a Circle:
- Definition: A segment is the region of a circle enclosed between a chord and the arc subtended by it.
- Area of Segment: The area $AsegmentA_{\text{segment}}$
  
  $A_{segment}$ of a segment is the difference between the area of the sector and the area of the triangular portion: $TriangleA_{\text{segment}} = A_{\text{sector}} – \text{Area of Triangle}$
  
  $A_{segment} = A_{sector} - Area of Triangle$
- Application: Used in problems involving areas within circular sectors and segments.
Application Problems:
- Example 1: Calculate the area of a sector with a radius of 7 cm and a central angle of 60°.
  - Solution: Use $Asector=60∘360∘⋅π⋅72A_{\text{sector}} = \frac{60^\circ}{360^\circ} \cdot \pi \cdot 7^2$
    
    $A_{sector} = 360 ^{\circ} 60 ^{\circ} \cdot π \cdot 7^{2}$ .
- Example 2: Find the area of a segment of a circle with a radius of 10 cm and a central angle of 120°, where the area of the sector is first computed and the area of the triangle is subtracted.
  - Solution: Compute the sector area and then subtract the area of the corresponding triangle.
Composite Figures:
- Example: Calculate the area of a composite figure formed by combining circular sectors and segments, or circles with other geometric shapes.
Real-Life Applications:
- Practical Uses: Applying area formulas in real-life situations such as designing circular gardens, calculating the surface area of round tables, or determining the paint needed for circular objects.

Quiz Structure:

The MCQ quiz for this chapter includes a series of questions designed to test students’ understanding of areas related to circles, including sectors and segments. Questions cover formulas, applications, and problem-solving techniques related to circular areas. The interactive format allows students to practice and assess their knowledge effectively.

Conclusion:

Practicing with the Class 10 Math Areas Related to Circles MCQ Test Chapter 11 is an excellent way for CBSE students to reinforce their understanding of circle-related area concepts. This chapter provides a comprehensive overview of the areas of circles, sectors, and segments, and their practical applications. The MCQ quiz helps ensure students are well-prepared for their academic assessments and competitive exams.

Sanjay Kumar

Math educator (6-12) with an MSc from Delhi University and quiz content creator at QuizRanker.org.