Find the best tutors and institutes for Class 10 Tuition
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 $\pi = 3.14$)
Solution :
Given Variables & Initial Setup
We are tasked with finding the total cost of polishing the top surface of a circular table. The following parameters are provided:
- Diameter of the circular table-top ($d$) = $1.6 \text{ m}$
- Rate of polishing ($R$) = $₹ 15 \text{ per m}^2$
- Constant approximation for $\pi$ = $3.14$
Step 1: Determining the Radius of the Circular Table-Top
The standard formula for the area of a circle requires the radius ($r$). The radius is defined as exactly half of the diameter [Per the fundamental geometric properties of a circle].
$r = \frac{d}{2}$
$r = \frac{1.6 \text{ m}}{2} = 0.8 \text{ m}$
Step 2: Calculating the Area of the Circular Region
Polishing is a surface-level operation, meaning we must calculate the two-dimensional area of the table-top. We apply the area formula for a circle [Derived from the integration of concentric circular rings, $A = \pi r^2$].
$A = \pi r^2$
Substituting the given values into the equation:
$A = 3.14 \times (0.8 \text{ m})^2$
First, square the radius:
$(0.8)^2 = 0.8 \times 0.8 = 0.64 \text{ m}^2$
Next, multiply by $\pi$:
$A = 3.14 \times 0.64 \text{ m}^2$
$A = 2.0096 \text{ m}^2$
The total area to be polished is exactly $2.0096 \text{ m}^2$.
Step 3: Computing the Total Cost of Polishing
The total cost ($C$) is the product of the total area and the rate of polishing per square meter. [Dimensional analysis confirms this operation: $\text{m}^2 \times \frac{₹}{\text{m}^2} = ₹$].
$C = \text{Area} \times \text{Rate}$
$C = 2.0096 \text{ m}^2 \times 15 \frac{₹}{\text{m}^2}$
Performing the multiplication:
$C = 30.144 \text{ ₹}$
In standard currency formatting, values are typically rounded to two decimal places (the nearest paisa). Therefore, $30.144$ rounds to $30.14$.
Final Solution: The total cost of polishing the circular table-top is ₹ 30.14.
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
- 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.
- 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 $\pi = \frac{22}{7}$)
- 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 $\pi = 3.14$)
CBSE Solutions for Class 9 Mathematics Coordinate Geometry
Chapters in CBSE - Class 9 Mathematics
Top Tutors who teach Coordinate Geometry
Depankar sir is a very interactive teacher he makes learning fun and effective.After studying with him for only 6 months I have shown signs of improvement. I would definitely recommend him go everyone
I have more than 15 years teaching experience in teaching CBSE classes 8-10 Physics/Chemistry. I can also teach math upto 9th . All my students secured 10/10 in previous years exams. And in school more than 90% students got more than 90 in Science Exam and all have passed in Science i. Physics and Chemistry.
I am so impressed with his teaching. Highly Recommended!!!
I have been teaching for seven years. . I am teaching maths for cbse, icse,IB (international baccalaureate)' usa and uk (precalculus, AP calculus, algebra) acdamic students up to 12 grade and students preparing for SAT, OLYMPIAD, engineering and IIT ENTRANCE . Besides this I am also teaching Physics and Chemistry. I love teaching. I have excellent communication skills, a good understanding of concepts, ability to motivate students. Since every student has a different understanding level so for me its essential to know in what way students will understand and to explain them quickly. I also like to help in teaching someone who is financially weak to get an education. I can assure you to give 100% results. I will give you free demo classes and Pay me only when you will be completely satisfied with my teaching. I am btech from IIT Delhi Now I am full time in teaching
Excellent teaching capability. Young and sincere. Always punctual in class timings wish him a lot of successes
I am a teacher of maths and science, having a experience of 8+ years in teaching, done my schooling from CBSe board and degree from IP university.
Till date taught 1200+ students preparing for board examinations in 10th standard, average result= 98.75% marks. Do you want YOUR child to excel too? Contact me at the earliest!
Very nice teacher. Most efficient in judging weakness in subject and in filling those knowledge gaps. Thank you so much for your support. Highly recommended to all.
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
- Chandigarh Mathematics Tutors
- Jaipur Mathematics Tutors
- Pune Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Surat Mathematics Tutors
Download free CBSE - Class 9 Mathematics Coordinate Geometry EXERCISE 9.2 worksheets
Download Now