Exercise 11.2: Area of Sector and Segment
Find the area of sectors (pizza slices) and segments (the region between a chord and an arc). Most board questions come from this exercise.
Extra Practice Questions
These questions cover the same concepts as Exercise 11.2. Try solving them to build confidence before or after the textbook exercise.
Ravi wants to find the length of the arc of a sector with radius 7 cm and angle 90°. He applies the formula: Arc Length = (90/360) × π(7)². What mistake did Ravi make?
A clock's minute hand is 10 cm long. How far does the tip of the minute hand move in 30 minutes? (Use π = 3.14)
A circle C1 is inscribed in an equilateral triangle of side 'a'. Another circle C2 is circumscribed about the same equilateral triangle. Find the ratio of the area of C1 to the area of C2.
Two circles of the same radius 'r' intersect each other such that each passes through the center of the other. Find the area of the common region (lens).
A square ABCD has side length 'a'. Four semi-circles are drawn *outwards* with each side of the square as diameter. Find the perimeter of the entire figure formed.
Which of the following statements is TRUE regarding a sector of a circle with radius 'r' and central angle 'θ' (in degrees)?
A chord of a circle of radius 14 cm subtends an angle of 90° at the centre. Find the area of the corresponding major segment. (Use π = 22/7)
Let ABC be a right-angled triangle with hypotenuse BC. Semi-circles are drawn externally on each side of the triangle as diameters. If the area of the semi-circle on AB is A1, on AC is A2, and on BC is A3, which of the following statements is always true?
If the perimeter of a semi-circular protractor is 36 cm, then its diameter is: (Use π = 22/7)
If the radius of a sector is increased by 25% and its central angle is decreased by 20%, what is the percentage change in its area?
Stuck on a question?
Paste any question from Exercise 11.2 into our AI Maths Solver and get a step-by-step solution instantly. It works for all NCERT questions.
Try AI Solver — FreeCommon Mistakes to Avoid
- ✗Confusing sector (two radii + arc) with segment (chord + arc)
- ✗Not converting the angle to use in the formula
- ✗Forgetting to subtract the triangle area to get the segment area
Other Exercises in Chapter 11
Frequently Asked Questions
What is the formula for area of a sector?
Area of sector = (θ/360°) × πr², where θ is the angle at the centre.
How many questions are in Exercise 11.2?
Exercise 11.2 has 14 questions on sectors, segments, and arc lengths.
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