Find the best tutors and institutes for Class 10 Tuition
Q1(b):
Find the circumference of the circles with the following radius: (Take $\pi = \frac{22}{7}$) (b) $28$ mm
Solution :
Given Variables & Initial Setup
We are tasked with determining the circumference of a circle given its radius. The fundamental parameters provided for this geometric system are:
- Radius of the circle, $r = 28 \text{ mm}$
- Approximation for Pi, $\pi = \frac{22}{7}$
Theoretical Foundation: Circumference of a Circle
The circumference ($C$) of a circle is defined as the continuous line forming the boundary of the closed geometric figure. [Per the geometric definition of a circle's perimeter in Euclidean space], the circumference is directly proportional to its radius, with the constant of proportionality being $2\pi$. The governing formula is:
$C = 2\pi r$
Step 1: Substitution of Values
We substitute the given values of $r$ and $\pi$ into the standard circumference formula:
$C = 2 \times \left(\frac{22}{7}\right) \times 28$
Step 2: Algebraic Simplification
To optimize the calculation, we first analyze the terms for common factors. The radius ($28$) is a multiple of the denominator ($7$) in our fractional value of $\pi$. [By the fundamental properties of rational numbers], we can divide $28$ by $7$ to simplify the expression before proceeding with multiplication:
$\frac{28}{7} = 4$
Substituting this simplified integer back into the equation yields:
$C = 2 \times 22 \times 4$
Step 3: Final Calculation
We now perform the sequential multiplication of the remaining scalar quantities:
First, multiply the constants:
$2 \times 22 = 44$
Next, multiply the result by the simplified radius factor:
$C = 44 \times 4$
$C = 176$
Since the radius was provided in millimeters ($\text{mm}$), the circumference, being a one-dimensional measure of length, must carry the identical unit.
Final Solution: The circumference of the circle is $176 \text{ mm}$.
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(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 ₹ $4$ 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 ₹ $15$. (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 ₹ $15/m^2$. (Take $\pi = 3.14$)
- 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 $\pi = \frac{22}{7}$)
CBSE Solutions for Class 9 Mathematics Coordinate Geometry
Chapters in CBSE - Class 9 Mathematics
Top Tutors who teach Coordinate Geometry
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
I have Taught 3 years in CBSE board and 5 years In ICSE board in class 10 with 100% results.Got an opportunity to go for CBSE board class 10 Maths copy correction.Was Board examiner head for ICSE .
Pragya ma'am is amazing! She helped me with maths a lot! Great teacher!
I am a strong believer in concept-based gain of knowledge. I start from scratch while teaching the very basic concepts and take my students to a level where they have a deep understanding of the subject. Once they understand the concept, the next step is that practice a lot of questions/numerical/problem in the class itself as practice is the key to retain knowledge. I always refer to prescribed books by CBSE/ICSE board but always encourage students to refer additional 1 or 2 books based on their speed to practice. In last I provide them enough homework to practice at home and send me the doubts before the next class. Also for 10th students, we prepare right from beginning by covering the previous year questions and this approach till date have been fruitful as most of my students excel in the board exams
My son is taking Math and Science Tuition with Rakesh sir for last 2 weeks. I am very much satisfied with his teaching techniques. He uses visual aids which helps the student in understanding the concepts in a better way.
22 Years Experience in Schools IN ICSE/CBSE/IGCSE IN DIFFERENT STATE BOARDS
Sir is very friendly teacher he will support us more he is the best teacher of the year his teaching skills are really good.
I teach Mathematics to students of Classes 8 to 10, and I have been guiding young learners for over 25 years. My teaching method focuses on helping students develop not just strong academic results, but also a deeper confidence and love for the subject. I hold an M.Sc. in Mathematics and a B.Ed., which have given me both mastery of the subject and the pedagogical skills to teach it effectively. In addition to this, I am a certified Vedic Math trainer, which allows me to introduce students to faster calculation techniques and enhance their mental math abilities. Over the course of my career, I have taught multiple age groups and ability levels, always with a focus on clarity and practice. I firmly believe that every student is capable of excelling in math if the concepts are explained in a structured and relatable way. My students’ consistent success reflects my dedication and effective teaching style. I offer both online and offline classes. Each session is designed with a well-structured lesson plan, ensuring that every topic is covered in depth and revised frequently. I use interactive discussions to ensure active participation and encourage students to voice their doubts without hesitation. I make use of PPTs and a whiteboard during my lessons to visually explain concepts and illustrate multiple approaches to problem-solving. Along with concept explanation, I include plenty of guided practice and gradual difficulty progression to boost skills and confidence. Regular assessment, practice worksheets, revision tests, and personal attention are key elements of my approach. Yes, I also provide study materials and additional exercises to ensure clarity and practice. My goal is to make mathematics an enjoyable part of every student's learning journey.
Find more Tutor for Coordinate Geometry 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 9 Mathematics Coordinate Geometry EXERCISE 9.2 worksheets
Download Now