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Become A Master of Mensuration - Areas related to Circles

High school math that covers Areas related to Circle in detail, with a step-by-step approach with formulae and solutions

Created byLakshmi Narayana

Last updated 11/2022

English

What you'll learn

Review of Concepts of Area and Perimeter of a Circle.
Areas of Sector and Segment of a Circle.
Circumference of Circle.
Length of an Arc of a Sector.
Perimeter of Sector.
Area of minor segment and major segment.
Areas of Combination of Plane Figures.
Applications of perimeter and Area of Sector, Segment and Circles.
At the end of the course, students will not only have learned about the topics in detail but also be able to solve various problems based on them.

Course content

10 sections • 69 lectures • 7h 56m total length

Introduction10:22
Introduction
Q 15:03
An athlete runs on a circular track of radius 49 m and covers a distance of 3080 m along its boundary. How many rounds has he taken to cover this distance? [Take π=22/7].
Q 27:41
The cost of fencing a circular field at the rate of ₹24 per metre is ₹5280. The field is to be ploughed at the rate of ₹0.50 per m2. Find the cost of ploughing the field[Take π =22/7].
Q 33:25
If the ratio of the circumferences of two circles is 3 : 1, then find the ratio of their areas.
Q 44:24
If the perimeter of a protractor is 72 cm, then calculate its area.
Test your understanding
Home Assignment

Introduction5:53
Sector and Areas of Sector
Q 12:29
In a circle of radius 21 cm, an arc subtends an angle of 600 at the centre. Find the area of sector formed by the arc. (Use π = (22 )/7)
Q 25:20
Find the area of the sector of a circle with radius 4 cm and of angle 30°. Also, find the area of the corresponding major sector (Use π = 3.14).
Q 33:21
What is the perimeter of a sector of a circle whose central angle is 90° and radius is 7 cm?
Q 44:40
Find the difference of the areas of a sector of angle 120° and its corresponding major sector of a circle of radius 21 cm.
Test your understanding
Home Assignment

Introduction4:23
Area of Segment of a Circle
Q 19:25
Find the area of the segment AYB shown in Fig., if radius of the circle is 21 cm and ∠AOB = 120°. (Use π = 22/7)
Q 25:50
In a circle with centre O and radius 5 cm, AB is a chord of length 5√3 cm. Find the area of sector AOB.
Q 35:52
A round table cover has six equal designs as shown in the given figure. If the radius of the cover is 35 cm then find the total area of the design. [Use √3 =1.732 and π= 3.14.]
Test your understanding
Home Assignment

Introduction2:21
Areas of Combinations of Plane Figures:
When combination of circle(or)semi-circle and square (or) rectangle are given
Q 18:18
In figure, two circular flower beds have been shown on two sides of a square lawn ABCD of side 56 m. If the centre of each circular flower bed is the point of intersection O of the diagonals of the square lawn, find the sum of the areas of the lawn and the flower beds.
Q 24:22
Find the area of the shaded region in figure, where ABCD is a square of side 14 cm.
Q 37:00
Find the area of the shaded design in figure, where ABCD is a square of side 10 cm and semicircles are drawn with each side of the square as diameter. (Use = 3.14)
Q 46:55
In the given figure, ABCD is a trapezium with AB‖DC, AB = 18 cm, DC = 32 cm and the distance between AB and DC is 14 cm. Circles of equal radii 7 cm with centres A, B, C and D have been drawn. Then, find the area of the shaded region of the figure.
(Use π = 22/7).
Test your understanding
Home Assignment

Introduction1:31
Areas of Combinations of Plane Figures: When combination of two concentric circles are given
Q 13:44
In the given figure, the area of the shaded region between two concentric circles is 286 cm2. If the difference of the radii of the two circles is 7 cm, find the sum of their radii.
Q 24:35
In the given figure, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and 3.5 cm with centre O. If ∠POQ = 30°, find the area of the shaded region.
Q 38:26
In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region. (Use π = 22/7)
Q 43:35
Nitika has a circular plot of radius 105 m. he donates a 7 m wide track along its boundary for community track. Find the area of the track. [Take,π=22/7]
Test your understanding
Home Assignment

Introduction1:16
Areas of Combinations of Plane Figures: When combination of circle and triangle are given
Q 16:50
Find the area of the shaded region in figure, if AC = 20 cm, AB = 15 cm and O is the centre of the circle.
Q 27:32
In the given figure, AOB is a sector of angle 60° of a circle with centre O and radius 17 cm. If AP ⊥ OB and AP = 15 cm, find the area of the shaded region.
Q 36:43
Find the area of the shaded region in figure, if BC = BD = 8 cm, AC = AD = 15 cm and O is the centre of the circle. (Take π = 3.14)
Q 43:51
A memento is made as shown in the figure. Its base PBCR is silver plated from the front side. Find the area which is silver plated.(π =(22 )/7)
Test your understanding
Home Assignment

Introduction1:21
Areas of Combinations of Plane Figures : When combination of quadrant of circle and triangle (or) square is given
Q 14:47
A square OABC is inscribed in a quadrant OPBQ of a circle as shown in the adjoining figure. If OA = 14 cm, find the area of the shaded region.
Q 28:35
In figure, ABC is a right-angled triangle at A. Semi-circles is drawn on AB, AC and BC as diameters. Find the area of the shaded region.
Q 34:04
In figure, APB and CQD are semicircles of diameter 7 cm each, while ARC and BSD are semicircles of diameter 14 cm each. Find the perimeter of the shaded region.
Q 48:39
Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in a given figure. Find the area of the shaded region.
Test your understanding

Q 15:12
The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.
Q 26:46
The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.
Q 319:46
Fig. 12.3 depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.
Q 410:30
The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?
Q 51:49
Tick the correct answer in the following and justify your choice : If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
(A) 2 units (B) p units (C) 4 units (D) 7 units

Q 12:42
Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.
Q 23:47
Find the area of a quadrant of a circle whose circumference is 22 cm.
Q 34:44
The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
Q 412:41
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 (ii) major sector. (Use π = 3.14)
Q 512:22
In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find:
(i) the length of the arc (ii) area of the sector formed by the arc
(iii) area of the segment formed by the corresponding chord
Q 611:12
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 = 3.14 and = 1.73)
Q 78:40
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 = 3.14 and = 1.73)
Q 89:47
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. 12.11). Find
(i) the area of that part of the field in which the horse can graze.
(ii) the increase in the grazing area if the rope were 10 m long instead of 5 m. (Use = 3.14)
Q 98:53
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. 12.12. Find :
(i) the total length of the silver wire required.
(ii) the area of each sector of the brooch.
Q 106:19
An umbrella has 8 ribs which are equally spaced (see Fig. 12.13). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.
Q 116:58
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.
Q 124:47
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 = 3.14)
Q 1311:14
A round table cover has six equal designs as shown in Fig. 12.14. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹ 0.35 per cm2. (Use √3 = 1.7)
Q 142:12
Tick the correct answer in the following :
Area of a sector of angle p (in degrees) of a circle with radius R is
(A) p/180 × 2πR (B) p/180 × πR2 (C) p/360 × 2πR (D) p/720 × 2πR2

Q 19:56
Find the area of the shaded region in Fig. 12.19, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.
Q 27:15
Find the area of the shaded region in Fig. 12.20, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and AOC = 40°.
Q 35:59
Find the area of the shaded region in Fig. 12.21, if ABCD is a square of side 14 cm and APD and BPC are semicircles.
Q 48:32
Find the area of the shaded region in Fig. 12.22, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.
Q 57:27
From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in Fig. 12.23. Find the area of the remaining portion of the square.
Q 611:45
In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in Fig. 12.24. Find the area of the design.
Q 76:47
In Fig. 12.25, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region.
Q 810:51
Fig. 12.26 depicts a racing track whose left and right ends are semi-circular.
The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find :
(i) the distance around the track along its inner edge
(ii) the area of the track.
Q 98:37
In Fig. 12.27, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.
Q 1014:39
The area of an equilateral triangle ABC is 17320.5 cm2. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (see Fig. 12.28). Find the area of the shaded region.
(Use π = 3.14 and √3 = 1.73205)
Q 117:04
On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.
Q 127:53
In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the
(i) quadrant OACB,
(ii) shaded region.
Q 139:21
In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use = 3.14)
Q 146:36
AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see Fig. 12.32). If ∠AOB = 30°, find the area of the shaded region.
Q 1512:29
In Fig. 12.33, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.
Q 168:20
Calculate the area of the designed region in Fig. 12.34 common between the two quadrants of circles of radius 8 cm each.

Requirements

Basic knowledge of fundamental operations -Addition, Subtraction, Product and Division.
Each chapter is inbuilt with prerequisite knowledge classes where the child gets immense knowledge and a clear understanding of the chapters.

Description

This course is carefully designed to explain various applications of Mensuration - Areas related to Circles.
It has 69 lectures spanning around eight hours of on-demand videos that are divided into 7 sessions. The course is divided into a simplified day-by-day learning schedule.
Each topic is divided into simple sessions and explained extensively by solving multiple questions. Each session contains a detailed explanation of the concept.
An online test related to the concept for immediate assessment of understanding.
Session-based daily home assignments with a separate key. The students are encouraged to solve practice questions and quizzes provided at the end of each session.
This course will give you a firm understanding of the fundamentals and is designed in a way that a person with little or no previous knowledge can also understand very well.
It covers 100% video solutions of the NCERT exercises , with selected NCERT exemplars and R D Sharma.
Our design meets the real classroom experience by following classroom teaching practices. We have designed this course by keeping in mind all the needs of students and their desire to become masters in math. This course is designed to benefit all levels of learners and will be the best gift for board-appearing students. Students love these easy methods and explanations. They enjoy learning maths and never feel that maths is troublesome.

Topics covered in the course:

Review of Concepts of Area and Perimeter of a Circle.
Areas of Sector and Segment of a Circle
Circumference of Circle
Length of an Arc of a Sector
Perimeter of Sector
Area of minor segment and major segment.
Areas of Combination of Plane Figures
Applications of perimeter and Area of Sector, Segment and Circles.

With this course you'll also get

Perfect your mathematical skills on Mensuration - Areas related to Circles.
A Udemy Certificate of Completion is available for download.

Feel free to contact me with any questions or clarifications you might have.

I can't wait for you to get started on mastering the real number systems.

I look forward to seeing you on the course! :)

Benefits of Taking this Course:

On completion of this course, one will have detailed knowledge of the chapter and be able to easily solve all the problems, which can lead to scoring well in exams with the help of explanatory videos ensure complete concept understanding.

Downloadable resources help in applying your knowledge to solve various problems.

Quizzes help in testing your knowledge. In short, one can excel in math by taking this course.

Who this course is for:

This course has been designed for students of the Grade 10th CBSE, ICSE, SSC, GCSE, IGCSE, SAT, ACT, GRE, and other board-appearing students and competitive exam aspirants.
Students studying for the public or other competitive examinations.
Home-school parents are looking for extra support with the fundamentals.
Anyone interested in revising or learning the basics of mathematics should.
Students in junior high and high school/secondary schools.
Anyone who wants to proficient mathematics and the solving different real life situations on Mensuration - Areas related to Circles well.
Anyone who wants to study math for fun after taking a break from school.
It will also benefit schools who wish to run classes in the absence of a teacher and make learning fun for their students.
It will also benefit teachers and schools who wish to improve their teaching skills and make learning fun for their students.
For 11th, 9th, and 8th grade students, this will help as a bridge course.

Become A Master of Mensuration - Areas related to Circles

What you'll learn

Explore related topics

Course content

Session 15 lectures • 31min

Session 25 lectures • 22min

Session 34 lectures • 26min

Session 45 lectures • 29min

Session 55 lectures • 22min

Session 65 lectures • 26min

Session 75 lectures • 27min

Exercise 12.15 lectures • 44min

Exercise 12.214 lectures • 1hr 46min

Exercise 12.316 lectures • 2hr 24min

Requirements

Description

Who this course is for: