Find the best tutors and institutes for Class 10 Tuition
Q1:
Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°. (Unless stated otherwise, use $\pi = \frac{22}{7}$)
Solution :
Given:
Radius of the circle ($r$) = $6\text{ cm}$
Angle of the sector ($\theta$) = $60^\circ$
Value of $\pi = \frac{22}{7}$
To find:
The area of the sector of the circle.
Step 1: State the formula for the area of a sector.
The area of a sector of a circle with radius $r$ and central angle $\theta$ (in degrees) is given by the formula:
$\text{Area of sector} = \frac{\theta}{360^\circ} \times \pi r^2$
[Justification: The area of a sector is a fraction of the total area of the circle ($\pi r^2$), where the fraction is determined by the ratio of the sector's angle to the total angle of a circle ($360^\circ$)]
Step 2: Substitute the given values into the formula.
Substituting $r = 6$, $\theta = 60^\circ$, and $\pi = \frac{22}{7}$:
$\text{Area} = \frac{60}{360} \times \frac{22}{7} \times (6)^2$
Step 3: Perform the arithmetic calculations.
First, simplify the fraction $\frac{60}{360}$:
$\frac{60}{360} = \frac{1}{6}$
[Since $60 \times 6 = 360$]
Next, calculate the square of the radius:
$6^2 = 36$
Now, substitute these back into the expression:
$\text{Area} = \frac{1}{6} \times \frac{22}{7} \times 36$
Step 4: Simplify the final expression.
$\text{Area} = \frac{1 \times 22 \times 36}{6 \times 7}$
Divide $36$ by $6$:
$\text{Area} = \frac{22 \times 6}{7}$
[Since $36 \div 6 = 6$]
$\text{Area} = \frac{132}{7}$
[Since $22 \times 6 = 132$]
Converting to decimal form (optional, but standard for verification):
$\text{Area} \approx 18.857\text{ cm}^2$
Final Answer: The area of the sector is $\frac{132}{7}\text{ cm}^2$ (or approximately $18.86\text{ cm}^2$).
More Questions from Class 10 Mathematics Areas Related to Circles EXERCISE 11.1
- Q10: An umbrella has 8 ribs which are equally spaced (see Fig. 11.10). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella. (Unless stated otherwise, use $\pi = \frac{22}{7}$)
- Q11: A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades. (Unless stated otherwise, use $\pi = \frac{22}{7}$)
- Q12: To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (Use $\pi = 3.14$)
- Q13: A round table cover has six equal designs as shown in Fig. 11.11. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ` 0.35 per cm$^2$. (Use $\sqrt{3} = 1.7$)
- Q14: Tick the correct answer in the following : Area of a sector of angle $p$ (in degrees) of a circle with radius $R$ is
- Q2: Find the area of a quadrant of a circle whose circumference is 22 cm. (Unless stated otherwise, use $\pi = \frac{22}{7}$)
- Q3: The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes. (Unless stated otherwise, use $\pi = \frac{22}{7}$)
- Q4(i): A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding : (i) minor segment (Use $\pi = 3.14$)
- Q4(ii): A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding : (ii) major sector. (Use $\pi = 3.14$)
- Q5(i): In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find: (i) the length of the arc (Unless stated otherwise, use $\pi = \frac{22}{7}$)
- Q5(ii): In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find: (ii) area of the sector formed by the arc (Unless stated otherwise, use $\pi = \frac{22}{7}$)
- Q5(iii): In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find: (iii) area of the segment formed by the corresponding chord (Unless stated otherwise, use $\pi = \frac{22}{7}$)
- Q6: A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use $\pi = 3.14$ and $\sqrt{3} = 1.73$)
- Q7: A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle. (Use $\pi = 3.14$ and $\sqrt{3} = 1.73$)
- Q8(i): A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see Fig. 11.8). Find (i) the area of that part of the field in which the horse can graze. (Use $\pi = 3.14$)
- Q8(ii): A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see Fig. 11.8). Find (ii) the increase in the grazing area if the rope were 10 m long instead of 5 m. (Use $\pi = 3.14$)
- Q9(i): A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in Fig. 11.9. Find : (i) the total length of the silver wire required. (Unless stated otherwise, use $\pi = \frac{22}{7}$)
- Q9(ii): A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in Fig. 11.9. Find : (ii) the area of each sector of the brooch. (Unless stated otherwise, use $\pi = \frac{22}{7}$)
CBSE Solutions for Class 10 Mathematics Areas Related to Circles
Chapters in CBSE - Class 10 Mathematics
Top Tutors who teach Areas Related to Circles
Super Tutor
Banjara Hills, Hyderabad
7 yrs of
Exp
16 students
612 hrs of classes completed
700
per hour
Online Classes
Student's Home
Over 6+ years, I've honed my craft as a mentor and educator to more than 100s of students, catalyzing their academic and personal development. My approach goes beyond traditional teaching, integrating experiential learning and technology to engage students and deepen comprehension. Through individualized attention and encouragement, I've guided countless students to exceed expectations, fostering a culture of achievement and self-discovery. Witnessing their transformative journeys, from overcoming challenges to embracing their potential, has been profoundly rewarding.
Vijay Sir is simply the best! He is incredibly knowledgeable and well-prepared. His passion for teaching 10th-grade Maths and Science shines through in every single lesson we have.
Top Tutor
MSR nagar mathikere, Bangalore
20 yrs of
Exp
21 students
5390 hrs of classes completed
499
per hour
Online Classes
I enjoy teaching and making things easier and fun for the children. Didn't send my kids for any tuitions. Today the elder child is a CSE graduate , working for Amazon & the other is in her 3rd year MBBS !
I have been studying Maths and Science under her guidance since 8th grade. She explains every concept in a simple and clear way, making even difficult topics easy to understand. Her teaching style is patient and supportive, and she always makes sure all doubts are cleared. She focuses on strengthening basics and gives regular practice, which has really helped me improve. Because of her guidance, my confidence in both subjects has increased a lot. I am truly grateful for her dedication and support
Super Tutor
Kodambakkam, Chennai
15 yrs of
Exp
57 students
3901 hrs of classes completed
800
per hour
Online Classes
With a decade of experience in teaching mathematics, physics, and chemistry for students from grades 8 through 12 across CBSE, IB, and ICSE boards, I offer a comprehensive educational approach that caters to a diverse range of curricula and learning needs. My academic background includes a BE and an MBA, equipping me with both technical and managerial skills that enhance my teaching methodology. Throughout my career, I have specialized in home tutoring, where I have developed a personalized approach to education that focuses on each student's unique needs and strengths. My sessions are designed to be interactive and engaging, fostering a learning environment where students feel supported and motivated. I conduct both online and offline classes, each lasting one hour, and utilize a variety of teaching tools to facilitate learning. I employ a whiteboard to visually explain concepts and provide question papers to help students practice and prepare for their exams. This hands-on approach ensures that students not only understand theoretical concepts but also develop problem-solving skills and confidence in their subjects. My commitment to delivering high-quality education and my extensive experience make me well-suited to guide students through their academic journey, helping them achieve their full potential in mathematics, physics, and chemistry.
Super Tutor
Pandri, Raipur
4 yrs of
Exp
10 students
2501 hrs of classes completed
575
per hour
Online Classes
Hello, my name is Atulya Kumar. I have completed my studies at IIT(ISM)_Dhanbad and I am currently pursuing a PhD at NIT-Rourkela. With a degree in engineering, I am dedicated to teaching. Since 2019, I have been teaching physics to JEE, NEET, and Class XI & XII board students. I take great pride in sharing that my students have achieved exceptional results, with some clearing NEET 2022 with an AIR of 2513 and NEET 2023 with an AIR of 1702. Additionally, many of my students have scored above the 98th percentile in JEE Mains 2023. Teaching physics is a personal challenge for me. I strive to create a comfortable learning environment where students can fully grasp the concepts and apply them effectively during examinations, resulting in excellent marks and ranks.
Super Tutor
BTM 6th Stage, Bangalore
11 yrs of
Exp
11 students
829 hrs of classes completed
600
per hour
Online Classes
Student's Home
With over 11 years of teaching experience, I have had the privilege of mentoring more than 5,000 students across various reputed coaching institutes in Bangalore. My teaching has primarily focused on preparing students for competitive exams, and I take pride in the fact that many of my students have successfully qualified for NEET, JEE and CET under my guidance. Throughout my career, I have been committed to delivering clear, concept-driven instruction while fostering a supportive and open classroom environment. I ensure that every student, regardless of their level, feels comfortable asking questions and engaging actively in the learning process. My ability to simplify complex topics and build strong student rapport continues to be the cornerstone of my teaching approach.
Find more Tutor for Areas Related to Circles in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
Download free CBSE - Class 10 Mathematics Areas Related to Circles EXERCISE 11.1 worksheets
Download Now
