Find the best tutors and institutes for Class 10 Tuition
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 $\pi = 3.14$)
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 $\pi = 3.14$)
Solution :
Given:
- A square-shaped grass field with side length $s = 15\text{ m}$.
- A horse is tied to one corner of the square field.
- The length of the rope, which acts as the radius $r$ of the grazing area, is $r = 5\text{ m}$.
To Find:
The area of the part of the field in which the horse can graze.
Step 1: Understanding the Geometry of the Grazing Area
Since the horse is tied to a corner of a square field, the angle at the corner of the square is $90^\circ$. The horse can move within a circular sector defined by the length of the rope. Therefore, the grazing area is a sector of a circle with radius $r = 5\text{ m}$ and central angle $\theta = 90^\circ$.
Step 2: Formula for the Area of a Sector
The formula for the area of a sector of a circle is given by:
$\text{Area of Sector} = \frac{\theta}{360^\circ} \times \pi r^2$
[Where $\theta$ is the central angle in degrees and $r$ is the radius of the circle.]
Step 3: Substituting the Given Values
Given values: $\theta = 90^\circ$, $r = 5\text{ m}$, and $\pi = 3.14$.
$\text{Area} = \frac{90^\circ}{360^\circ} \times 3.14 \times (5)^2$
Step 4: Performing the Calculation
First, simplify the fraction:
$\frac{90}{360} = \frac{1}{4}$
Next, calculate the square of the radius:
$(5)^2 = 25$
Now, substitute these back into the equation:
$\text{Area} = \frac{1}{4} \times 3.14 \times 25$
$\text{Area} = \frac{78.5}{4}$
$\text{Area} = 19.625\text{ m}^2$
Final Answer: The area of the part of the field in which the horse can graze is 19.625 m².
More Questions from Class 10 Mathematics Areas Related to Circles EXERCISE 11.1
- 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 $\pi = \frac{22}{7}$)
- 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(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 $\pi = \frac{22}{7}$)
- 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
CBSE Solutions for Class 10 Mathematics Areas Related to Circles
Chapters in CBSE - Class 10 Mathematics
Top Tutors who teach Areas Related to Circles
Top Tutor
Antop Hill, Mumbai
10 yrs of
Exp
2 students
50 hrs of classes completed
350
per hour
Online Classes
I am a teacher of Mathematics and Physics. I have been teaching since my college days. After completing my college I ran a coaching institute in my home town Nainital. During that time I got selected in Income Tax department through Staff Selection Commission. As teaching has always been my passion so I continued teaching students online. Currently, I give tuitions to CBSE/ICSE students of Class IX & X on one-on-one and batch bases. I prepare students for competitive Exams like SSC CGL, Banks, Railways etc. Since Mathematics and Science of IX & X standard play a significant role in cracking competitive exams. Every student no matter from what stream has to face that competition in future. Therefore, I prepare and polish student in a way which help them a lot in a future of competitive environment. Apart from this I also take classes for Vedic Maths and Fast calculating tricks.
Top Tutor
Sector-21, Chandigarh
6 yrs of
Exp
150
per hour
Online Classes
Student's Home
Tutor's home
All the concepts are taught well and doubts are resolved at the earliest. Each student gets personal attention.for in depth knowledge and concept clarity , students of targeted classes may contact. M well experienced, qualified teacher and tutor with over ,6 years of experience in teaching maths and chemistry across different boards including cbse ,icse M a passionate teacher helping hundreds of students to overcome their fear from maths nd chemistry
Top Tutor
Govindpuri Shiva Colony, Jaipur
10 yrs of
Exp
23 students
1478 hrs of classes completed
500
per hour
Online Classes
Tutor's home
I am a teacher of mathematics. I am giving online tuitions and tuitions at my home in Jaipur(Rajasthan). I have done M.Sc. , B.Ed. in mathematics. I have experience of 10 years of teaching mathematics , Vedic Mathematics and Olymiads.
I Shivani. N feel the class handled by Rohit Sir is a lively, interactive and also class room teaching experience with individual attention. I am looking forward to take weekly tests after which I will share my feed back on it. Thank you Sir.
Super Tutor
Kharghar Sector 27, Mumbai
13 yrs of
Exp
30 students
1081 hrs of classes completed
650
per hour
Online Classes
Student's Home
**Teaching Methodology:** My approach to teaching Mathematics and Science is personalized and interactive. I focus on understanding each student's unique learning style and adapt my methods accordingly. My goal is to make Maths and Science relatable and engaging, using real-life examples and practical applications to enhance understanding.I try to develop self thinking on problem and pushing them to solve by self **Key Skills:** - Strong grasp of Mathematics concepts across various levels - Ability to simplify complex topics for better understanding - Excellent communication and motivational skills - Patient and supportive, ensuring a comfortable learning environment - Regular progress assessments and constructive feedback **Services Offered:** - One-on-one personalized tutoring sessions - Homework and assignment assistance - Exam preparation and revision classes - Online and in-person tutoring options - Flexible scheduling to accommodate student needs **Achievements:** - Helped students improve their grades by an average of [25%] - Successfully prepared students for competitive exams with [JEE,NEET,IMO] - Received positive feedback and high ratings from students and parents Interested in improving your Maths AND Science skills? Contact me today to schedule a session and take the first step towards mastering Mathematics and Science!
This teacher is incredibly friendly and teaches in a very calm and patient manner. He helped me clear all my doubts; after failing my board exams previously, I managed to score 47/80 in Mathematics under his guidance. He truly excels at building a student's confidence.
Top Tutor
Thane West, Thane
16 yrs of
Exp
17 students
3974 hrs of classes completed
350
per hour
Online Classes
This is Debabrato Chatterjee, an Maths and Science tutor with more than fifteen years of experience. I have been and am teaching students of IB, IGCSE, CBSE, ICSE, and Maharastra State Boards. My teaching style is to learning from concepts and their application. Solving many papers and completing homework helps grasp the concepts. I teach students from grade VI to XII. Please let me know when you would like to schedule a demo.
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
- Ghaziabad Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
Download free CBSE - Class 10 Mathematics Areas Related to Circles EXERCISE 11.1 worksheets
Download Now
