# NCERT Class 10 Mathematics Chapter 11 Areas Related to Circles: Summary, Concepts, and Revision Notes | SwaVid

This chapter extends your understanding of circles beyond basic circumference and area. It delves into calculating areas of specific parts of a circle,...

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# Areas Related to Circles

## Concepts in this chapter

## The ideas this chapter keeps returning to

## Where this chapter usually trips people up

## Find the gaps before this chapter finds them for you.

## Related chapters

### Perimeter and Area of a Circle (Review)

Chapter 11 · Class 10 Mathematics

This chapter extends your understanding of circles beyond basic circumference and area. It delves into calculating areas of specific parts of a circle, such as sectors and segments, and then applies these concepts to find areas of complex figures formed by combining circles with other plane figures. Mastery of these concepts is crucial for solving real-world problems involving circular designs and regions.

Your study route

Key topics

This section revisits the fundamental formulas for the circumference (perimeter) and area of a circle. The circumference is the distance around the circle, given by 2πr, and the area is the space enclosed by the circle, given by πr², where 'r' is the radius.

Example

Find the area of a circle whose circumference is 22 cm. (This type of problem helps recall basic formulas and their interrelation).

Watch out

Students often mix up the formulas for circumference and area, or incorrectly use diameter instead of radius in calculations.

This section revisits the fundamental formulas for the circumference (perimeter) and area of a circle. The circumference is the distance around the circle, given by 2πr, and the area is the space enclosed by the circle, given by πr², where 'r' is the radius.

Tap the card for an example

Example

Find the area of a circle whose circumference is 22 cm. (This type of problem helps recall basic formulas and their interrelation).

Why it matters

These are the foundational building blocks for all subsequent calculations involving parts of a circle. Without a firm grasp of these, understanding sectors and segments is impossible.

Watch out

Students often mix up the formulas for circumference and area, or incorrectly use diameter instead of radius in calculations.

Ask at home

Ask your child to state the formulas for circumference and area of a circle and explain when to use each. Give a simple radius (e.g., 7 cm) and ask them to calculate both values.

This chapter builds upon the basic knowledge of circles from previous classes, focusing on calculating areas of specific parts of a circle and composite figures. It revisits the formulas for the circumference and area of a circle. The core of the chapter introduces concepts like sectors and segments. Students learn to derive and apply formulas for the area of a sector and the length of an arc, understanding their dependence on the radius and the central angle. Subsequently, the area of a segment is explained as the difference between the area of the corresponding sector and the area of the triangle formed by the radii and the chord. A significant part of the chapter involves applying these concepts to find areas of complex figures formed by combining circles, sectors, and other basic geometric shapes like squares, triangles, and rectangles. Mastery of these concepts is crucial for solving practical problems involving circular designs and regions.

Chapter summary

This chapter builds upon the basic knowledge of circles from previous classes, focusing on calculating areas of specific parts of a circle and composite figures. It revisits the formulas for the circumference and area of a circle. The core of the chapter introduces concepts like sectors and segments. Students learn to derive and apply formulas for the area of a sector and the length of an arc, understanding their dependence on the radius and the central angle. Subsequently, the area of a segment is explained as the difference between the area of the corresponding sector and the area of the triangle formed by the radii and the chord. A significant part of the chapter involves applying these concepts to find areas of complex figures formed by combining circles, sectors, and other basic geometric shapes like squares, triangles, and rectangles. Mastery of these concepts is crucial for solving practical problems involving circular designs and regions.

What you should learn

Keep these close

Circumference of a circle = 2πr.

Area of a circle = πr².

A sector is a region bounded by two radii and an arc.

Area of a sector with angle θ (in degrees) = (θ/360°) × πr².

Length of an arc with angle θ (in degrees) = (θ/360°) × 2πr.

A segment is a region bounded by a chord and an arc.

Area of minor segment = Area of corresponding sector - Area of triangle formed by radii and chord.

Area of major segment = Area of circle - Area of minor segment.

Area of a quadrant = (1/4)πr².

For combined figures, break them into simpler known shapes and add/subtract areas.

Remember to use consistent units for all measurements (e.g., all in cm or all in m).

The value of π is usually 22/7 or 3.14, as specified in the problem statement.

Common confusions

It is easy to think

Confusing the formulas for circumference and area of a circle.

The clearer idea

Circumference measures the boundary (a length, 1D), while Area measures the surface enclosed (a region, 2D). Remember '2πr' for length and 'πr²' for area.

It is easy to think

Always assuming the triangle formed by the chord and radii is equilateral or right-angled when calculating segment area, regardless of the central angle.

The clearer idea

The angle of the triangle at the center is the same as the central angle of the sector. The area of the triangle depends on this angle (e.g., (1/2)r²sinθ for a general triangle, or (1/2)base×height for specific cases like 90°).

It is easy to think

Forgetting to subtract the area of the triangle from the sector area when calculating the area of a minor segment.

The clearer idea

A minor segment is the region of the sector *minus* the triangle formed by the radii and the chord. Visualize the shape to ensure you are calculating the correct region.

It is easy to think

Incorrectly identifying the parts of a combined figure, leading to wrong addition or subtraction of areas.

The clearer idea

Carefully shade the required area and identify the basic geometric shapes that compose it. Draw auxiliary lines if needed to separate or complete shapes, and clearly decide whether to add or subtract their areas.

It is easy to think

Using the wrong value for π or not being consistent with units throughout a problem.

The clearer idea

Always check the problem statement for the value of π to be used (e.g., 22/7 or 3.14). Ensure all lengths are in the same unit (cm, m, etc.) before performing any calculations to avoid errors.

Before you push ahead

Most stuck chapters trace back to one earlier idea. Check the prerequisites first, or let SwaVid adapt this chapter to the way your child learns.

Keep exploring Class 10

Source

- Recall and apply formulas for circumference and area of a circle.
- Calculate the area of a sector and the length of an arc of a circle.
- Determine the area of a segment of a circle.
- Solve problems involving areas of combinations of plane figures that include circles or parts of circles.
- Understand the relationship between angle, radius, arc length, and sector area.
- Recall and apply formulas for circumference and area of a circle.
- Calculate the area of a sector and the length of an arc of a circle.
- Determine the area of a segment of a circle.
- Solve problems involving areas of combinations of plane figures that include circles or parts of circles.
- Understand the relationship between angle, radius, arc length, and sector area.
- NCERT Class 10 Mathematics textbook: Mathematics : Chapter 11: Areas Related to Circles

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- [10 Circles Theorem 10.1: Perpendicularity of Radius and Tangent · Number of Tangents from a Point to a Circle Open chapter](https://swavid.com/maths/class/10/chapter/circles)
- [12 Surface Areas and Volumes Review of Basic Solid Formulas · Surface Area of a Combination of Solids Open chapter](https://swavid.com/maths/class/10/chapter/surface-areas-and-volumes)
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- [NCERT Class 10 Mathematics textbook: Mathematics](https://ncert.nic.in/textbook.php)