Here 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, πa^{2} cm^{2}? 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
∴ Area of circle = pr^{2} = 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 C_{1} and C_{2} be the two circles with radii r and 2r, respectively.
According to the question,
Therefore, angle of the corresponding sector of circle, C_{1} is double the angle of the corresponding sector of circle C_{2}.
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 pb^{2} 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 p^{2} cm^{2}? Why?
Answer. False
Explanation:
Let ABCD be a square inscribed in a circle of diameter p cm.
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