Areas Related to Circles: Sector Area MCQs Quiz | Class 10
This quiz is designed for **Class X** students, covering **Mathematics (Code 041)** from **Unit VI: Mensuration**. Specifically, it focuses on **Areas Related to Circles: Sector Area**, including the area of a sector and its application in various problems. Attempt all 10 multiple-choice questions, then submit to see your score and download a detailed answer PDF for revision.
Understanding Areas Related to Circles: Sector Area
This section provides a deeper understanding of the concepts tested in the quiz, focusing on the area of a sector of a circle and its applications. A sector is a part of a circle enclosed by two radii and an arc, much like a slice of pizza. Calculating its area is a fundamental skill in geometry and has various real-world applications.
Key Concepts and Formulas
The area of a sector is directly proportional to the angle subtended at the center. If the angle is ‘theta’ (in degrees) and the radius of the circle is ‘r’, the formula for the area of the sector is:
Area of Sector = (theta / 360) * pi * r2
Where ‘pi’ is a mathematical constant approximately equal to 3.14159 or 22/7.
Related to the sector is the length of the arc. The formula for the length of an arc of a sector is:
Length of Arc = (theta / 360) * 2 * pi * r
The perimeter of a sector includes the two radii and the arc length: Perimeter = 2r + Arc Length.
Important Points and Applications
- Understanding the relationship between the angle of the sector and the full circle (360 degrees) is crucial.
- The value of pi (22/7 or 3.14) should be used as specified in the problem.
- Clock Problems: The minute hand of a clock sweeps a sector. In 60 minutes, it completes 360 degrees, so in 1 minute, it sweeps 6 degrees. The hour hand sweeps 0.5 degrees per minute.
- Area of Segment: While not the primary focus of this quiz, the area of a segment (the region between a chord and its corresponding arc) can be found by subtracting the area of the triangle formed by the radii and the chord from the area of the corresponding sector.
Quick Revision Table: Circle vs. Sector
| Feature | Circle | Sector (angle theta) |
|---|---|---|
| Radius | r | r |
| Angle at Center | 360 degrees | theta |
| Area Formula | pi * r2 | (theta / 360) * pi * r2 |
| Perimeter/Circumference | 2 * pi * r | (theta / 360) * 2 * pi * r + 2r |
Practice Questions
Here are some additional practice questions to reinforce your understanding. Try to solve them on your own!
- A sector of a circle with radius 10 cm has an arc length of 11 cm. Find the area of the sector. (Use pi = 22/7)
- The minute hand of a clock is 15 cm long. What is the area swept by the minute hand in 20 minutes? (Use pi = 3.14)
- If the area of a sector of a circle with radius 7 cm is 77 cm square, find the angle of the sector. (Use pi = 22/7)
- A circle has a radius of 6 cm. If the area of a sector is 9 pi cm square, what is the angle of the sector?
- The perimeter of a sector of a circle with radius 21 cm is 64 cm. Find the area of the sector. (Use pi = 22/7)
Mastering these concepts will help you excel in the ‘Areas Related to Circles’ unit of Class X Mathematics.
Content created and reviewed by the CBSE Quiz Editorial Team based on the latest NCERT textbooks and CBSE syllabus. Our goal is to help students practice concepts clearly, confidently, and exam-ready through well-structured MCQs and revision content.