Maths · Mensuration · chapter 11 of 14
Class 10 Maths Chapter 11: Areas Related to Circles Assertion-reason questions with answers
2 assertion-reason questions on Areas Related to Circles, each with its answer and the reason, written from the NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter. Each question gives an Assertion (A) and a Reason (R); choose how they stand to each other.
Question 1
Assertion (A): The area of a quadrant of a circle of radius r is 14πr². Reason (R): The area of a sector of angle θ in a circle of radius r is θ360 × πr².
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Answer: (a) Both A and R are true, and R is the correct explanation of A.
A quadrant is a sector of angle 90°, and (90/360)πr² = πr²/4, so R gives A.
Question 2
Assertion (A): If two radii of a circle make an angle of 60°, the triangle they form with the chord joining their ends is equilateral. Reason (R): If the minor sector has angle θ, the major sector has angle 360° − θ.
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Answer: (b) Both A and R are true, but R is not the correct explanation of A.
A is true: the triangle is isosceles with a 60° apex, so all angles are 60°. R is true but is about sector angles, not the triangle.
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