1. Home
  2. |  
  3. CBSE Board |  

NCERT Exemplar Solution for Class 10 Maths: Areas Related to Circles (Part-II)

Aug 22, 2017 10:43 IST

    Class 10 Mathematics NCERT Exemplar, NCERT Exemplar Solution, Constructions Class 10 NCERT ExemplarHere you get the CBSE Class 10 Mathematics chapter 11, Areas Related to Circles: NCERT Exemplar Problems and Solutions (Part-II). This part of the chapter includes solutions for questions in exercise 11.2 of NCERT Exemplar Problems for Class 10 Mathematics Chapter: Areas Related to Circles. This exercise comprises of only the Very Short Answer Type Questions framed from various important topics in the chapter. Each question is provided with a detailed solution.

    CBSE Class 10 Mathematics Syllabus 2017-2018

    NCERT Exemplar problems are a very good resource for preparing the critical questions like Higher Order Thinking Skill (HOTS) questions. All these questions are very important to prepare for CBSE Class 10 Mathematics Board Examination 2017-2018 as well as other competitive exams.

    Find below the NCERT Exemplar problems and their solutions for Class 10 Mathematics Chapter, Areas Related to Circles:

    Exercise 11.2

    Very Short Answer Type Questions:

    Write whether True or False and justify your answer.

    Question. 1 Is the area of the circle inscribed in a square of side a cm, πa2 cm2? Give reasons for your answer.

    Answer. False

    Explanation:

    Let a circle with centre O and radius r  be inscribed in a square ABCD with side a.

    Question. 2 Will it be true to say that the perimeter of a square circumscribing a circle of radius a cm is 8a cm? Give reason for your answer.

    Answer. True

    Explanation:

    Question. 3 In figure, a square is inscribed in a circle of diameter d and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Give reason for your answer.

    Thus, the area of the outer square is two times the area of the inner square.

    Hence, given statement is false.

    Question. 4 Is it true to say that area of segment of a circle is less than the area of its corresponding sector? Why?

    Answer. False

    Explanation:

                                                                                  

    It is true only in the case of minor segment. But in case of major segment, it is always greater than the area of sector.

    Question. 5 Is it true that the distance travelled by a circular wheel of diameter d cm in one revolution is 2πd cm? Why?

    Answer. False

    Explanation:

    Distance travelled by the wheel in one revolution = Circumference of wheel = 2πr = πd    [∵2r = d]                                                              

    Hence, the given statement is false.

    Question. 6 In covering a distance s m, a circular wheel of radius r m makes s/2pr revolution. Is this statement true? Why?

    Answer. Yes, this statement is true.

    Explanation:

    Question. 7 The numerical value of the area of a circle is greater than the numerical value of its circumference. Is this statement true? Why?

    Answer. No.

    Explanation:

    For 0 < r < 2, then numerical value of circumference is greater than numerical value of area of circle

    Let the radius, r = 1

    &there4; Area of circle = pr2 = p (1)2 = p

    And circumference of circle = 2pr = 2p (1) = 2p

    Thus, the area of a circle is less than its circumference.

    Question. 8 If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r, then the angle of the corresponding sector of the first circle is double the angle of the corresponding

    sector of the other circle. Is this statement false? Why?

    Answer. No, this statement is true.

    Explanation:

    Let C1 and C2 be the two circles with radii r and 2r, respectively.

    According to the question,

    Therefore, angle of the corresponding sector of circle, C1 is double the angle of the corresponding sector of circle C2.

    Question. 9 The area of two sectors of two different circles with equal corresponding arc lengths are equal. Is this

    statement true? Why?

    Answer. False

    Explanation:

    Since, area of a sector is given as,

    Hence, the areas of two sectors with equal corresponding arc lengths, would be same in case both the circles have equal radii.

    Question. 10 The areas of two sectors of two different circles are equal. Is it necessary that their

    corresponding arc lengths are equal? Why?

    Answer. False

    Explanation:

    As the area of a sector is given as,

    Hence, the areas of two sectors of two different circles would be equal only in case both the circles have equal radii and equal corresponding arc lengths.

    Question. 11 Is the area of the largest circle that can be drawn inside a rectangle of length a cm and

    breadth b cm (a> b)is pb2 cm? Why?

    Answer. False

    Explanation:

    Let a circle with centre O be the largest possible circle drawn inside a rectangle ABCD of length a cm and breadth b cm

    Question. 12 Circumference of two circles are equal. Is it necessary that their areas be equal? Why?

    Answer. True

    Explanation:

    Given, circumference of two circles are equal.

    Therefore, two circles with equal radii will also have equal areas.

    Hence, if circumference of two circles are equal, then their corresponding radii will also be equal. So, their areas will also be equal.

    Question. 13 Areas of two circles are equal. Is it necessary that their circumferences are equal? Why?

    Answer. True

    Explanation:

    Given, areas of two circles are equal.

    Therefore, two circles with equal radii will have equal circumferences.

    Hence, if areas of two circles are equal, then their corresponding radii are equal. So, their circumference will also be equal.

    Question. 14 Is it true to say that area of a square inscribed in a circle of diameter p cm is p2 cm2? Why?

    Answer. False

    Explanation:

    Let ABCD be a square inscribed in a circle of diameter p cm.  

    CBSE Class 10 NCERT Textbooks & NCERT Solutions

    NCERT Solutions for CBSE Class 10 Maths

    NCERT Exemplar Problems and Solutions Class 10 Science: All Chapters

    Latest Videos

    Register to get FREE updates

      All Fields Mandatory
    • (Ex:9123456789)
    • Please Select Your Interest
    • Please specify

    • ajax-loader
    • A verifcation code has been sent to
      your mobile number

      Please enter the verification code below

    This website uses cookie or similar technologies, to enhance your browsing experience and provide personalised recommendations. By continuing to use our website, you agree to our Privacy Policy and Cookie Policy. OK
    X

    Register to view Complete PDF