Chapter 11: Areas Related to Circles
The Master Hub: 25 Unique Conceptual Pillars extracted from CBSE Board Exam Papers (2022–2026). Strictly filtered for logic-traps, case studies, and advanced applications.
Sector Area to Arc Length Algebra
If the arc length of a sector is \(l\) and the radius of the circle is \(r\), find the area of the sector in terms of \(l\) and \(r\).
Wheel Revolutions (Distance)
The diameter of a wheel is 63 cm. The distance travelled by the wheel in 100 revolutions is...
Sector Area from Arc Length
Find the area of a sector of a circle of radius 28 cm and arc length 10.8 cm.
The Olympic Rings Decomposition
Case Study: The Olympic symbol comprises five interlocking rings. Calculate the area of the 8 minor segments formed by the intersections...
Tied Animals Grazing
Three horses are tied with 7 m long ropes at the three corners of a triangular field. Find the total area grazed by them.
Major Segment at 90°
A chord of a circle of radius 10 cm subtends a right angle at the center. Find the area of the corresponding major segment.
Clock Minute Hand Sector
The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
Perimeter of a Sector (A/R)
Assertion: The perimeter of a sector of a circle of radius r and central angle ΞΈ is (ΞΈ/360) × 2Οr + 2r.
Minor Segment at 60°
Find the area of the minor segment of a circle of radius 12 cm, if the corresponding chord subtends an angle of 60° at the center.
Perimeter = Area Algebra
If the perimeter and the area of a circle are numerically equal, then the radius of the circle is...
Conservation of Area (Pythagoras)
Two circles of radii 8 cm and 6 cm are melted to form a single circle. Find the radius of the new circle.
Area Ratio & Geometric Probability
A circle is inscribed in a square. Find the ratio of the area of the circle to the area of the square.
The Clover Margin Region
Find the area of the shaded clover region enclosed between four circles of radius 7 cm touching each other externally.
Inscribed Circle Area Algebra
Calculate the area of the largest circle that can be drawn inside a square of side 14 cm.
Semi-Circular Disc Algebra
The area of a semi-circular disc whose diameter is 'd', is represented by...
The Semi-Circle Perimeter Trap
If the area of a semi-circular field is 15400 sq. m, then the perimeter of the field is...
Twin Circles in a Rectangle
A rectangle of dimensions 20 cm × 10 cm contains two identical circles inscribed side-by-side. Find the area of the shaded region.
Algebraic Reversal for Central Angle (ΞΈ)
A sector of a circle with area 264/7 cm² is cut from a circle of radius 6 cm. The central angle of the sector is...
Pure Arc Length Formula
The length of the arc of the sector of a circle with radius 21 cm and of central angle 60° is:[cite: 209, 424]
Hour Hand Angle Sweep
The hour hand of a clock is 7 cm long. The angle swept by it between 7:00 a.m. and 8:10 a.m. is:[cite: 209, 424]
The Silver Brooch Case Study
Case Study: A brooch is crafted from silver wire in the shape of a circle with a diameter of 35 cm. The wire is also used to create 5 diameters...[cite: 219, 434]
The 120-Degree Segment Perimeter
In the given figure, chord AB subtends an angle of 120° at the centre...[cite: 351, 566]
Equal Slices Shortcut
A circle is divided into 16 identical sectors. If radius of the circle is 7 cm, area of each sector is:[cite: 490, 589]
Composite Sectors Addition
In the given figure, three sectors of a circle of radius 5 cm, making angles 35°, 50° and 95° at the centre are shaded. Find the area of the shaded region.[cite: 260, 600]
The Farmer's Inscribed House
A farmer has a circular piece of land. He wishes to construct his house in the form of largest possible square within the land.[cite: 813, 814]
