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# NCERT Solutions for Class 10 Maths Chapter 12 : Areas Related to Circles

Area related to Circle Class 10 NCERT Solutions Maths Chapter 12 are made strictly in accordance with the CBSE Curriculum and the exam pattern. NCERT Solutions for Areas related to Circles Class 10 are curated by our team of subject experts at Toppr in a detailed manner. The NCERT textbook questions are answered in a way to provide you with a better understanding of the concepts in a systematic and step-by-step manner. It also contains the appropriate diagrams to explain the concepts to the students. As Class 10 exams are Board exams, these solutions will not only help the students in preparing for the board exams but also for the Olympiads. NCERT Solutions provided by Toppr are the best study material to excel in the exams. Also, the MCQs and long and short questions are all answered according to the weightage and the exam pattern. With the help of NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles you can also test your subject knowledge and analyze your shortcomings and work on them before the exams. These are the best resources designed after proper study and research and study to help the students in scoring good marks.

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## Access NCERT Solutions for Class 10 Maths Chapter 12 : Areas Related to Circles

Exercise 12.1
Question 1
The radii of two circles are and respectively. Find the radius of the circle which has a circumference equal to the sum of the circumferences of the two circles.
Medium
Solution
Verified by Toppr
Let the radius of required circle
As per the question
Circumference of the required circle Sum of circumference of two circles
Circumference of small circle

Circumference of small circle

Now,
Circumference of the required circle Sum of circumference of two circles
Hence, radius of new circle is 28 cm.
Question 3
Fif. 12.3 depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red,Blue,Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.
Medium
Solution
Verified by Toppr
SOLUTION:
GIVEN:

Diameter of Gold region= 21 cm
21/2= 10.5 cm

Area of Gold Region = πr²
= π(10.5)² =( 22/7)×  110.25 = 346.5 cm²
cm²

Radius for gold + red region= 10.5 + 10.5= 21 cm
Area of Red Region = π²(21² - 10.5²)

[Area of a ring= π (R²-r²), where R= radius of outer ring & r= radius of inner ring]

= 22/7 (21² – 10.5²)        [ a²-b²= (a+b)(a-b)]
= 22/7 (21 + 10.5)(21 – 10.5)
= (22/7 )x 31.5 x 10.5 = 1039.5 cm²

1039.5 cm²

Radius of blue region = Now radius for gold + red+ blue region= 21+10.5= 31.5 cm

Area of Blue Region = π(31.5² – 21²)
= 22/7 (31.5² - 21²)
= 22/7 (31.5 +21)(31.5 - 21)
= (22/7 )x 52.5 x 10.5 = 1732.5 cm²

cm²

Now,
radius for gold + red+ blue + black region= 31.5+10.5= 42 cm

Area of Black Region = π(42² – 31.5²)

= 22/7 (42²-31.5² )
= 22/7 (42+31.5)(42-31.5)
= (22/7 )x 73.5 x 10.5 = 2425.5 cm²

cm²

Now
radius for gold + red+ blue + black+ white region= 42+10.5= 52.5 cm

Area of White Region= π(52.5² – 42²)
= 22/7 (52.5²-42² )
= 22/7 (52.5+42)(52.5-42)
= (22/7 )x 94.5 x 10.5 = 3118.5 cm²

cm²

Exercise 12.2
Question 1
Question 3
The length of the minute hand of a clock is 14cm. find the area swept by the minute hand in 15 min.
Medium
Solution
Verified by Toppr
Minute hand completes full circle degree in minutes.
Angle swept by minute in minutes
Angle swept by the minute hand in minutes
Therefore,
Length of minute hand
Area swept by minute hand in minutes Area of sector
As we know that area of sector is given as-
Therefor,
Area swept by the minute hand in minutes
Hence the area swept by the minute hand in minutes is .
Hence the correct answer is .
Question 6
A chord of a circle of radius subtends an angle of at the centre. Find the areas of the corresponding minor and major segments of the circle.
(Use and )
Medium
Solution
Verified by Toppr
In the mentioned figure,
is the centre of circle,
is a chord
is a major arc,
Arc subtends an angle at

Area of sector

Area of minor segment (Area of Shaded region) Area of sector Area of

By trigonometry,

And,

cm

cm

Area of

Area of minor segment (Area of Shaded region)

Area of major segment Area of circle Area of minor segment

Question 7
A chord of a circle of radius 12 cm subtends an angle of  at the centre. Find the area of the corresponding segment of the circle.(Use  and
Medium
Solution
Verified by Toppr
Given that:-

To find:-

Area of segment
Solution:-

Area of sector

Let M be the point on such that

Now in and ,

By R.H.S. congruency,

Now by CPCT,

Therefore,

Now in right angled

Now, from , we have

Now, area of will be-

Area of segment

Hence the aea of the corresponding segment of the circle is .
Question 8
A horse is tied to a peg at one corner of a square shaped grass field of side by means of a long rope. Find
(i) the area of that part of the field in which the horse can graze.
(ii) The increase in the grazing area if the rope were long instead of . (Use )
Medium
Solution
Verified by Toppr
Side of square

The area available for horse to graze is nothing but "Area of Quadrant of a circle'

If the length of rope is increased to then the new radius ,

Increase in grazing area
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## NCERT Solutions for Areas related to Circles Class 10

Class 10 Maths Chapter 12 Areas Related to Circles explains the concepts of perimeter or circumference and area of a circle, parts of circles, their measurements and areas of plane figures. The chapter also discusses the concepts of area and perimeter of various polygons. This chapter is a part of Mensuration and has a weightage of around 10 marks in the exams. It also highlights the application of the formula of area and perimeter of the circle. It also covers the problems related to finding the radii of a circle that covers the area or perimeter of the sum area or perimeter covered by two other circles, finding the area of rings, and also the calculation of distance covered in revolutions. NCERT solutions for class 10 also apply this knowledge in finding the areas of sector and segment. The area and perimeter of a circle depend on the angle subtended by the arc at the centre of the circle. The chapter helps the students in solving the application based problems by enhancing their ability to pull out the angle subtended. Areas Related to Circles Class 10 also contains a lot of questions based on how to divide the circle equally. It also discusses the technique to find the angle of each equally divided arc and segments formed by umbrella or sectors when a regular polygon is inscribed in a circle. The chapter also deals with the numerical problems that involve calculating the area of various designs and patterns using many plane figures and polygons.

### Key Features of NCERT Solutions for Class 10 Maths Chapter 12 - Areas Related to Circles

• Class 10 NCERT Solutions are provided in a step-by-step manner with appropriate diagrams.
• The solutions provide a better understanding of the subject and concepts.
• These are curated by the experts after thorough research.
• They are the best means to evaluate your preparations and overcome your shortcomings.
• The Class 10 NCERT Solutions will help the students in board exams as well as Olympiads.