PYQs
Practise questions grouped by chapter and source year.
Practice questions are organised using the years and labels in our source collection. Work through the solutions with your teacher; these are not a complete official examination paper.
Practice question 1
Source year: 20252 marksArea of sector with radius 6cm, angle 60°. [CBSE 2025]
Practice question 2
Source year: 20243 marksHorse tied to corner of 15m square by 7m rope. [CBSE 2024]
Practice question 3
Source year: 20252 marksFind area of sector of circle with radius 6cm and central angle 60°. [CBSE 2025]
Practice question 4
Source year: 20243 marksA horse is tied to one corner of square plot of side 15m by rope 7m long. Find area it can graze. [CBSE 2024]
Practice question 5
Source year: 20233 marksFind perimeter of shaded region if ABCD is square of side 14cm and semicircles are drawn on each side. [CBSE 2023]
Practice question 6
Source year: 20222 marksArea of circle is 154cm². Find circumference. [CBSE 2022]
Formulae
Revisit important relationships and quick revision formulae.
Sector Area
A = (θ/360) × πr²
Circle Formulas
Area = πr²\nCircumference = 2πr\nDiameter = 2r
Sector Formulas
Area of sector = (θ/360°) × πr²\nLength of arc = (θ/360°) × 2πr\nwhere θ is central angle in degrees
Segment Formulas
Area of segment = Area of sector - Area of triangle
Derivations
Work through the reasoning behind key concepts.
Sector Area Formula
Area of full circle = πr² for angle 360°. For sector with angle θ°, area is proportional: Area = (θ/360°) × πr². Similarly, arc length = (θ/360°) × 2πr.
Sector Area Derivation
Area of full circle = πr² for 360°\nFor angle θ°: Area = (θ/360) × πr²
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