Find the best tutors and institutes for Class 10 Tuition
Q9:
Shazli took a wire of length $44$ cm and bent it into the shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? (Take $\pi = \frac{22}{7}$)
Solution :
Given Variables & Initial Setup
We are given a single continuous wire of a fixed length that is bent into two different geometric shapes (a circle and a square) in separate scenarios. The fundamental principle governing this problem is the Conservation of Perimeter, which states that the total boundary length of any shape formed by the wire must equal the total length of the wire.
- Total length of the wire, $L = 44 \text{ cm}$
- Mathematical constant, $\pi = \frac{22}{7}$
Step 1: Analyzing the Circular Shape and Finding the Radius
When the wire is bent into the shape of a circle, the entire length of the wire forms the boundary of the circle. [Per the geometric definition of circumference, the perimeter of a circle is its circumference].
Let $r$ be the radius of the circle. The formula for the circumference $C$ is:
$C = 2\pi r$
Equating the circumference to the total length of the wire:
$2\pi r = 44$
Substituting the given value of $\pi$:
$2 \left( \frac{22}{7} \right) r = 44$
$\frac{44}{7} r = 44$
Isolating $r$ by multiplying both sides by $\frac{7}{44}$:
$r = 44 \times \frac{7}{44}$
$r = 7 \text{ cm}$
Step 2: Calculating the Area of the Circle
The area $A_{circle}$ enclosed by a circle is given by the formula:
$A_{circle} = \pi r^2$
Substituting $r = 7 \text{ cm}$ and $\pi = \frac{22}{7}$:
$A_{circle} = \frac{22}{7} \times (7)^2$
$A_{circle} = \frac{22}{7} \times 49$
$A_{circle} = 22 \times 7$
$A_{circle} = 154 \text{ cm}^2$
Step 3: Analyzing the Square Shape and Finding the Side Length
When the same wire is bent into the shape of a square, the total length of the wire forms the perimeter of the square. [Per the properties of regular polygons, a square has four sides of equal length].
Let $s$ be the side length of the square. The formula for the perimeter $P$ of a square is:
$P = 4s$
Equating the perimeter to the total length of the wire:
$4s = 44$
Isolating $s$ by dividing both sides by $4$:
$s = \frac{44}{4}$
$s = 11 \text{ cm}$
Step 4: Calculating the Area of the Square
The area $A_{square}$ enclosed by a square is given by the formula:
$A_{square} = s^2$
Substituting $s = 11 \text{ cm}$:
$A_{square} = (11)^2$
$A_{square} = 121 \text{ cm}^2$
Step 5: Visualizing and Comparing the Enclosed Areas
We now compare the calculated areas to determine which geometric figure maximizes the enclosed space for a given perimeter (an application of the Isoperimetric Inequality).
- Area of the Circle: $154 \text{ cm}^2$
- Area of the Square: $121 \text{ cm}^2$
Since $154 \text{ cm}^2 > 121 \text{ cm}^2$, the circle encloses a significantly larger area than the square.
Final Solution: The radius of the circle is $7 \text{ cm}$ and its area is $154 \text{ cm}^2$. When bent into a square, the length of each side is $11 \text{ cm}$ and its area is $121 \text{ cm}^2$. Comparing the two, the circle encloses more area than the square.
More Questions from Class 9 Mathematics Coordinate Geometry EXERCISE 9.2
- Q1(a): Find the circumference of the circles with the following radius: (Take $\pi = \frac{22}{7}$) (a) $14$ cm
- Q1(b): Find the circumference of the circles with the following radius: (Take $\pi = \frac{22}{7}$) (b) $28$ mm
- Q1(c): Find the circumference of the circles with the following radius: (Take $\pi = \frac{22}{7}$) (c) $21$ cm
- Q10: From a circular card sheet of radius $14$ cm, two circles of radius $3.5$ cm and a rectangle of length $3$ cm and breadth $1$cm are removed. (as shown in the adjoining figure). Find the area of the remaining sheet. (Take $\pi = \frac{22}{7}$)
- Q11: A circle of radius $2$ cm is cut out from a square piece of an aluminium sheet of side $6$ cm. What is the area of the left over aluminium sheet? (Take $\pi = 3.14$)
- Q12: The circumference of a circle is $31.4$ cm. Find the radius and the area of the circle? (Take $\pi = 3.14$)
- Q13: A circular flower bed is surrounded by a path $4$ m wide. The diameter of the flower bed is $66$ m. What is the area of this path? ($\pi = 3.14$)
- Q14: A circular flower garden has an area of $314$ m$^2$. A sprinkler at the centre of the garden can cover an area that has a radius of $12$ m. Will the sprinkler water the entire garden? (Take $\pi = 3.14$)
- Q15: Find the circumference of the inner and the outer circles, shown in the adjoining figure? (Take $\pi = 3.14$)
- Q16: How many times a wheel of radius $28$ cm must rotate to go $352$ m? (Take $\pi = \frac{22}{7}$)
- Q17: The minute hand of a circular clock is $15$ cm long. How far does the tip of the minute hand move in $1$ hour. (Take $\pi = 3.14$)
- Q2(a): Find the area of the following circles, given that: (a) radius = $14$ mm (Take $\pi = \frac{22}{7}$)
- Q2(b): Find the area of the following circles, given that: (b) diameter = $49$ m
- Q2(c): Find the area of the following circles, given that: (c) radius = $5$ cm
- Q3: If the circumference of a circular sheet is $154$ m, find its radius. Also find the area of the sheet. (Take $\pi = \frac{22}{7}$)
- Q4: A gardener wants to fence a circular garden of diameter $21$ m. Find the length of the rope he needs to purchase, if he makes $2$ rounds of fence. Also find the cost of the rope, if it costs â‚ą $4$ per meter. (Take $\pi = \frac{22}{7}$)
- Q5: From a circular sheet of radius $4$ cm, a circle of radius $3$ cm is removed. Find the area of the remaining sheet. (Take $\pi = 3.14$)
- Q6: Saima wants to put a lace on the edge of a circular table cover of diameter $1.5$ m. Find the length of the lace required and also find its cost if one meter of the lace costs â‚ą $15$. (Take $\pi = 3.14$)
- Q7: Find the perimeter of the adjoining figure, which is a semicircle including its diameter.
- Q8: Find the cost of polishing a circular table-top of diameter $1.6$ m, if the rate of polishing is â‚ą $15/m^2$. (Take $\pi = 3.14$)
CBSE Solutions for Class 9 Mathematics Coordinate Geometry
Chapters in CBSE - Class 9 Mathematics
Top Tutors who teach Coordinate Geometry
Super Tutor
Badarpur, Delhi
11 yrs of
Exp
146 students
3625 hrs of classes completed
200
per hour
Online Classes
Tutor's home
I am utterly grateful to Akshay sir for his unending support and sincere guidance. He was such a big pillar of support in my board exams and his style of teaching is truly exceptional!!!! His notes, his previous year questions, his tips and his advices are really helpful for the board exams. I was able to score 97.2% in my boards because of his style of teaching. In fact all the topics he marked as important came in the board exams! Moreover he is a very hardworking and dedicated teacher with an unending passion to support and tutor children. I really am grateful to you Akshay sir Regards Nirvaan Rai Batch 2025-26
Super Tutor
Kodambakkam, Chennai
15 yrs of
Exp
57 students
3783 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
Nerul Sector 20, Thane
10 yrs of
Exp
62 students
2814 hrs of classes completed
1200
per hour
Online Classes
I have done b.Tech in electrical engineering from IIT KANPUR. I taught one year in akash institute patna, 2 years in fiitjee patna. Currently I am teaching in unacademy. I have taught more than 6000 jee and neet aspirants. In which more than 500 students are selected in iitand aiims. If some one is interested to improve their physics upto jee advanced level take help with me .And see the magic. I can help students in their all type of assignment from any institute like allen, fiitjee, narayna, akash, resonance. I can help students to solve both volume of h.C verma within two month if some one is intrested in solving I.E.Irodov join me and see the next level of physics. My way of teaching is so easy and so advanced that student will realyy enjoy it. Don't waste your time in making decision just join and experience my level
He is a very dedicated teacher with excellent knowledge on topic. He knows Subject very well and teach accordingly to kids.
Super Tutor
Basaveshwara Nagar, Bangalore
12 yrs of
Exp
13 students
3347 hrs of classes completed
600
per hour
Online Classes
With over 15 years of dedicated teaching experience, I am an accomplished and qualified educator specializing in Spoken English, Math, Science, Social Science, and Kannada Language. My expertise extends across various educational boards, including CBSE, ICSE, and state boards. Passionate about unraveling the mysteries of mathematical problems and chemical equations. I have garnered recognition with the prestigious Best Teacher Award for orchestrating state-level Science exams. Having contributed my skills to the esteemed MaxMuller Public School in Bangalore, I am committed to fostering a nurturing and inspiring learning environment. Join me on this educational journey where knowledge meets enthusiasm!
Enrolled my 10-year-old for math tutoring, and the improvement is remarkable. The tutor identifies weak spots quickly, like multiplication tables. Fun drills with timers make practice competitive and enjoyable. She explains errors without blame, turning mistakes into lessons. Custom worksheets align with his CBSE curriculum spot-on. Confidence boost evident; he volunteers answers in class now. Test scores rose steadily over two months. Responsive to parent queries, even on weekends. Affordable rates for such quality one-on-one attention. Planning long-term enrollment—excellent choice!
Super Tutor
Katira Maharaja Hata, Arrah
4 yrs of
Exp
24 students
1777 hrs of classes completed
700
per hour
Online Classes
Tutor's home
I've been teaching Class 10th students of schools from India and abroad. I primarily work with them to prepare for Olympiad, JEE foundation and school exams. I've been teaching students of class 8th-10th Science and Mathematics for more than 3 years. So far, I have taught more than 100 students from India and abroad. I teach international students Mathematics, Physics and Chemistry. I teach almost all boards of India such as CBSE, ICSE and state boards. I also teach IGCSE and IB students. I've my offline coaching institute where I am teaching students of CBSE and state boards who require help in Science and Mathematics. Fee displayed on my profile is for 1Ă—1 classes. For group classes, the fee is substantially reduced.
Find more Tutor for Coordinate Geometry in your City
- Delhi Mathematics Tutors
- Bangalore Mathematics Tutors
- Hyderabad Mathematics Tutors
- Chennai Mathematics Tutors
- Kolkata Mathematics Tutors
- Mumbai Mathematics Tutors
- Noida Mathematics Tutors
- Pune Mathematics Tutors
- Gurgaon Mathematics Tutors
- Lucknow Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Jaipur Mathematics Tutors
