[Class 10] Assertion (A): If the radius of sector of circle is reduced

Question 20 Statement A (Assertion): If the radius of sector of a circle is reduced to its half and angle is doubled then the perimeter of the sector remains the same. Statement R (Reason): The length of the arc subtending angle θ at the centre of a circle of radius r =𝜋𝑟𝜃/180 (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true.Checking Assertion If the radius of sector of a circle is reduced to its half and angle is doubled then the perimeter of the sector remains the same. Now, Perimeter of sector = Length of arc + 2 × Radius = 𝜃/360 × (2𝜋𝑟)+2r = 𝜋𝜽𝒓/𝟏𝟖𝟎 +𝟐𝐫 Now, New Radius = R = r/2 New Angle = θ = 2θ New Perimeter of sector = 𝜋𝜃𝑅/180 +2𝑅 = 𝜋2𝜃(𝑟/2)/180 +2(r/2) = 𝝅𝜽𝒓/𝟏𝟖𝟎 +𝒓 But this not the same as original perimeter So, Assertion is false Checking Reason The length of the arc subtending angle θ at the centre of a circle of radius r =𝜋𝑟𝜃/180 Formula of length of an arc is Length of Arc = 𝜽/𝟑𝟔𝟎 × (𝟐𝝅𝒓) = 𝜋𝑟𝜃/180 Which same as mentioned in reasoning Thus, Reason is true. So, Assertion is false Reasoning is true So, the correct answer is (d)

Question 20 - CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

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