‘रचना-प्रयोग’ का मुख्य उद्देश्य क्या है?

व्याकरण का व्यावहारिक प्रयोग सिखाना

‘द्वितीयः’ किस प्रकार की संख्या है?

क्रमवाचक (दूसरा)

Write the formula for the area of a sector of angle \(\theta\).

\(\dfrac{\theta}{360^\circ} \times \pi r^2\), where \(r\) is the radius.

What is the difference between a sector and a segment?

A sector is bounded by two radii and an arc; a segment is bounded by a chord and an arc.

What is a sector of a circle?

The region enclosed by two radii of the circle and the arc between them (refer to the figure in your NCERT textbook).

Write the formula for the area of a sector of angle \(\theta\).

Area of sector \(= \dfrac{\theta}{360^\circ} \times \pi r^2\).

Write the formula for the length of an arc of angle \(\theta\).

Length of arc \(= \dfrac{\theta}{360^\circ} \times 2\pi r\).

What is a segment of a circle?

The region enclosed by a chord and the arc corresponding to it.

Find the area of a sector of radius 7 cm and angle \(90^\circ\). (Take \(\pi = 22/7\).)

Area \(= \dfrac{90}{360} \times \dfrac{22}{7} \times 7^2 = \dfrac{1}{4} \times 154 = 38.5\) cm\(^2\).

How do you find the area of the major sector if the minor sector’s area is known?

Subtract the area of the minor sector from the total area of the circle \((\pi r^2)\).

How is the area of a combination of plane figures found?

By adding or subtracting the areas of the basic figures (circles, sectors, triangles, rectangles) that make up the combined shape.

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CBSE Class 10 — Notes, Chapters & Practice Quizzes

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Chapter 11: Areas Related to CirclesClass 10 Mathematics — summary, notes, extra questions & NCERT solutions

Q: Write the formulae for the circumference and area of a circle of radius r.

Circumference \(= 2\pi r\) and area \(= \pi r^2\).

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The circumference of a circle of radius r is:

Summary

This chapter computes lengths and areas associated with circles and their parts. Building on the circumference \((2\pi r)\) and area \((\pi r^2)\) of a circle, it introduces the sector — a “slice” bounded by two radii and an arc — and the segment, bounded by a chord and an arc. Formulae for the length of an arc and the area of a sector in terms of the central angle let students find areas of these regions, and combined figures are handled by adding or subtracting the relevant areas. The chapter connects geometry with measurement in everyday shapes.

Perimeter and area of a circleArea of a sectorArea of a segmentAreas of combinations of figures

Key terms

Circumference

The perimeter of a circle, \(2\pi r\).

Sector

The region between two radii and the arc between them.

Segment

The region between a chord and its arc.

Area of a sector

\(\dfrac{\theta}{360^\circ} \times \pi r^2\), where \(\theta\) is the central angle.

Extra questions & answers

EXERCISE 11.1

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Area of a sector

Radius (cm)Angle (°)

Sector area =38.48cm²

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Circumference

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Meaning1 / 4

The perimeter of a circle, \(2\pi r\).

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Chapter 11: Areas Related to CirclesClass 10 Mathematics — summary, notes, extra questions & NCERT solutions

Summary

Key terms

Extra questions & answers

EXERCISE 11.1

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Practice quiz · Areas Related to Circles

Your Class 10 board-year rhythm

A little every day

Board-pattern practice

Results you can show off