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Areas Related to Circles

Karnataka Board · Class 10 · Mathematics

Flashcards for Areas Related to Circles — Karnataka Board Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.

45 questions20 flashcards5 concepts

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20 Flashcards
Card 1Sector Area

Find the area of a sector with radius 6 cm and central angle 60°. Use π = 22/7.

Answer

Step 1: Use formula Area = (θ/360°) × πr² Step 2: Area = (60°/360°) × (22/7) × 6² Step 3: Area = (1/6) × (22/7) × 36 Step 4: Area = (22 × 36)/(7 × 6) = 792/42 = 132/7 Step 5: Area = 18.86 cm² (approxi…

Card 2Segment Area

A chord of radius 10 cm subtends a right angle (90°) at the center. Find the area of the minor segment. Use π = 3.14.

Answer

Step 1: Area of segment = Area of sector - Area of triangle Step 2: Area of sector = (90°/360°) × π × 10² = (1/4) × 3.14 × 100 = 78.5 cm² Step 3: For right triangle with two sides = radius = 10 cm Ste…

Card 3Arc Length

Find the length of arc of a sector with radius 14 cm and central angle 45°. Use π = 22/7.

Answer

Step 1: Use formula Arc length = (θ/360°) × 2πr Step 2: Arc length = (45°/360°) × 2 × (22/7) × 14 Step 3: Arc length = (1/8) × 2 × (22/7) × 14 Step 4: Arc length = (1/8) × (44 × 14)/7 Step 5: Arc leng…

Card 4Formula Application

When do you use the formula Area = (θ/360°) × πr²?

Answer

Use this formula to find the AREA OF A SECTOR. Where: θ = central angle in degrees, r = radius Example: Sector with r = 5 cm, θ = 72° Area = (72°/360°) × π × 5² = (1/5) × 25π = 5π cm² Remember: This g…

Card 5Special Cases

Find the area of a quadrant (quarter circle) with radius 7 cm. Use π = 22/7.

Answer

Step 1: Quadrant means θ = 90° Step 2: Use sector formula: Area = (θ/360°) × πr² Step 3: Area = (90°/360°) × (22/7) × 7² Step 4: Area = (1/4) × (22/7) × 49 Step 5: Area = (22 × 49)/(7 × 4) = 1078/28 =…

Card 6Real-world Applications

A minute hand of length 12 cm sweeps for 15 minutes. Find the area covered.

Answer

Step 1: In 60 minutes, minute hand makes 360° Step 2: In 15 minutes, angle = (15/60) × 360° = 90° Step 3: Area swept = sector area with θ = 90°, r = 12 cm Step 4: Area = (90°/360°) × π × 12² Step 5: A…

Card 7Major Sector

Find the area of major sector when minor sector has area 50 cm² and radius is 10 cm. Use π = 3.14.

Answer

Step 1: Total circle area = πr² = 3.14 × 10² = 314 cm² Step 2: Major sector area = Total area - Minor sector area Step 3: Major sector area = 314 - 50 = 264 cm² Alternative method: Step 4: Find θ of m…

Card 8Segment Area - Complex

A chord subtends 120° at center of circle with radius 21 cm. Find the area of minor segment. Use π = 22/7, √3 = 1.73.

Answer

Step 1: Area of segment = Area of sector - Area of triangle Step 2: Sector area = (120°/360°) × (22/7) × 21² = (1/3) × (22/7) × 441 = 462 cm² Step 3: For triangle: Draw perpendicular from center to ch…

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Frequently Asked Questions

What are the important topics in Areas Related to Circles for Karnataka Board Class 10 Mathematics?
Areas Related to Circles covers several key topics that are frequently asked in Karnataka Board Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Areas Related to Circles — Karnataka Board Class 10 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.
How many flashcards are available for Areas Related to Circles?
There are 20 flashcards for Areas Related to Circles covering key definitions, formulas, and concepts. Use them daily for 10–15 minutes for best results.

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