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Chapter 11 maths class 10 Areas related to circles are a key concept in mathematics that play an important role in understanding various geometric properties. It involves calculating the area of circles and solving related problems using formulas for circumference, radius, and diameter. This topic of class10 math chapter 11 also extends to applications like sectors, segments, and the area of a circle within different types of planes. Whether you're a beginner or looking to strengthen your understanding, this article will break down complex topics into simpler parts and help you solve a variety of questions related to class 10 chapter 11 area related to circle.
Additionally, we will address some common questions students often face in class 10th math chapter 11, such as:
NCERT Solutions or Class 10 Maths Chapter 11, area related to Circles, created by experts at Careers360, provides detailed and step-by-step solutions that make learning easier for students preparing for the CBSE Class 10 board exams. The solutions cover all exercises in the NCERT solutions for Class 10 Maths and offer accessible, downloadable study material for a thorough understanding of the topic of class 10th maths chapter 11. By following the provided solutions, students can master the concepts related to circles and solve any problems of class 10 chapter 11 maths with confidence.
Also Read,
Circumference of a Circle: Circumference =
Where
Area of a Circle: Area =
Length of an Arc of a Sector - To find the length of an arc within a sector of a circle, given the radius 'r' and the angle in degrees 'θ', the formula is
Arc Length =
Area of a Sector of a Circle - For calculating the area of a sector within a circle with radius 'r' and angle in degrees 'θ', the formula is
Sector Area =
Area of a Segment of a Circle - The area of a segment of a circle can be found by subtracting the area of the corresponding triangle from the area of the corresponding sector.
Segment Area = Sector Area - Triangle Area
Segment Area =
When considering the distance (
Number Of Revolutions = Distance Travelled / circumference =
Free download NCERT Solutions for Class 10 Maths Chapter 11 Areas Related to Circles PDF for CBSE Exam.
NCERT Solutions for Maths Chapter 11 Area Related To Circle Class 10 Exercise: 11.1
We know that the area of a sector having radius r and angle
Thus, the area of the given sector is:-
Q2. Find the area of a quadrant of a circle whose circumference is 22 cm.
We are given the circumference of the circle.
Thus,
Also, we know that the area of a sector is given by :
It is given that we need to find the area of a quadrant thus
Hence, the area becomes:-
The minute hand rotates 360 degrees in one hour.
We need to find rotation in 5 min. :-
The area of the sector is given by :
Hence, the area swept by the minute hand in 5 minutes is
(ii) major sector. (Use π = 3.14)
(i)The angle in the minor sector is 90 o
Thus, the area of the sector is given by:-
Now the area of a triangle is:-
Thus, the area of the minor segment = Area of the sector - The area of a triangle
(ii)The area of the major sector can be found directly by using the formula :
In this case, the angle is 360o - 90o = 270o.
Thus, the area is: -
Q5. In a circle of radius 21 cm, an arc subtends an angle of 60° at the center. Find:
(ii) area of the sector formed by the arc
(iii) the area of the segment formed by the corresponding chord.
(i)The length of the arc is given by:-
Hence, the length of the arc is 22 cm.
(ii) We know that the area of the sector is given by:-
Thus, the area of the sector is 231 cm2.
(iii) For the area of the segment, we need to subtract the area of the triangle attached to the area of the arc.
Thus, consider the triangle:-
It is given that the angle of the arc is 60°, or we can say that all angles are 60 ° (since the two sides are equal). Hence, it is an equilateral triangle.
The area of the triangle is:-
Hence, the area of the segment is:-
The area of the sector is :
Now consider the triangle; the angle of the sector is 600.
This implies that it is an equilateral triangle. (As two sides are equal, they will have the same angle. This is possible only when all angles are equal i.e., 60°).
Thus, the area of the triangle is:-
Hence area of the minor segment :
The area of the major segment is :
For the area of the segment, we need the area of the sector and the area of the associated triangle.
So, the area of the sector is :
Now, consider the triangle:-
Draw a perpendicular from the center of the circle on the base of the triangle (let it be h).
Using geometry, we can write,
Similarly,
Thus, the area of the triangle is :
Hence, the area of the segment is:
Q8. A horse is tied to a peg at one corner of a square-shaped grass field of side 15 m using a 5 m long rope (see Fig). 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 10 m long instead of 5 m. (Use
(i)The part grazed by the horse is given by = Area of sector
(ii)When the length of the rope is 10 m, the area grazed will be:-
Hence, the change in the grazing area is given by :
(i) the total length of the silver wire required.
(ii) the area of each sector of the brooch.
(i)The total wire required will be for 5 diameters and the circumference of the brooch.
The circumference of the brooch:-
Hence the total wire required will be:-
(ii)
The total number of lines present in the brooch is 10 (line starting from the center).
Thus, the angle of each sector is 36°.
The area of the sector is given by:-
It is given that the umbrella has 8 ribs so the angle of each sector is 45°.
Thus, the area of the sector is given by:-
Hence, the area between two consecutive ribs is
The area cleaned by one wiper is:-
Hence, the required area (area cleaned by both blades) is given by:-
The area of the sector is given by:-
In this case, the angle is 80 o .
Thus, the area is:-
Q13. A round table cover has six equal designs as shown in Fig. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs. 0.35 per cm2. (Use
The angle of each of the six sectors is 60° at the center.
The area of the sector is given by:-
And the area of the equilateral triangle associated with the segment:-
Hence the area of segment is :
Thus the total area of design is :
So, the total cost for the design is:-
Q14. Tick the correct answer in the following :
The area of a sector of angle p (in degrees) of a circle with radius R is
(A)
(B)
(C)
(D)
We know that the area of the sector is given by:-
Hence, option (D) is correct.
Enhanced Conceptual Understanding: These ch 11 class 10 maths solutions serve as a valuable tool for students seeking to grasp circle-related concepts thoroughly.
Visual Clarity: The class 10 maths ch 11 solutions are thoughtfully supplemented with diagrams, facilitating a more interactive and comprehensive learning journey.
Accessible Language: The language employed in these chapter 11 maths class 10 solutions is intentionally straightforward, ensuring that students can easily grasp the content.
Step-by-Step Guidance: The chapter 11 maths class 10 solutions follow a methodical, step-by-step approach, aiding students in building a strong foundation and understanding the fundamentals with ease.
Individualized Learning: Students have the flexibility to tackle complex problems at their own pace, which fosters self-directed learning and builds problem-solving skills.
Resource Diversity: These ch 11 class 10 maths solutions open doors for students to explore NCERT solutions across various classes and subjects.
Expertly Crafted: These ch 11 class 10 maths solutions are meticulously prepared by experienced educators at Careers360, who prioritize providing clarity on key concepts and nurturing students' problem-solving abilities.
Also, students can get solutions for extracurricular-
As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters
NCERT Class 10 Maths Solutions - Chapter Wise
Chapter No. | Chapter Name |
Chapter 1 | |
Chapter 2 | |
Chapter 3 | |
Chapter 4 | |
Chapter 5 | |
Chapter 6 | |
Chapter 7 | |
Chapter 8 | |
Chapter 9 | |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | Areas Related to Circles |
Chapter 13 | |
Chapter 14 | |
Chapter 15 |
The length of an arc in a circle with radius
If the angle
Arc Length
The area of a segment is found by subtracting the area of the triangle from the sector's area:
Using the sector formula:
The triangle's area can be determined using trigonometry or Heron's formula.
A sector is a portion of a circle (like a pizza slice). Its area is given by:
where
A segment is the part of a circle enclosed by a chord and its corresponding arc, whereas a sector includes the central angle and two radii.
The area of a segment is found by subtracting the area of the triangle formed by the chord from the area of the sector:
- Gardens \& parks - Calculating circular flower beds and paths.
- Clocks \& dials - Dividing time into equal parts.
- Pizza \& cakes - Cutting equal slices.
- Sports fields - Designing semicircular goal areas in stadiums.
- Wheels \& tires - Measuring rolling distance and coverage area.
Hello
Since you are a domicile of Karnataka and have studied under the Karnataka State Board for 11th and 12th , you are eligible for Karnataka State Quota for admission to various colleges in the state.
1. KCET (Karnataka Common Entrance Test): You must appear for the KCET exam, which is required for admission to undergraduate professional courses like engineering, medical, and other streams. Your exam score and rank will determine your eligibility for counseling.
2. Minority Income under 5 Lakh : If you are from a minority community and your family's income is below 5 lakh, you may be eligible for fee concessions or other benefits depending on the specific institution. Some colleges offer reservations or other advantages for students in this category.
3. Counseling and Seat Allocation:
After the KCET exam, you will need to participate in online counseling.
You need to select your preferred colleges and courses.
Seat allocation will be based on your rank , the availability of seats in your chosen colleges and your preferences.
4. Required Documents :
Domicile Certificate (proof that you are a resident of Karnataka).
Income Certificate (for minority category benefits).
Marksheets (11th and 12th from the Karnataka State Board).
KCET Admit Card and Scorecard.
This process will allow you to secure a seat based on your KCET performance and your category .
check link for more details
https://medicine.careers360.com/neet-college-predictor
Hope this helps you .
Hello Aspirant, Hope your doing great, your question was incomplete and regarding what exam your asking.
Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.
hello Zaid,
Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.
best of luck!
According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.
You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.
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