Areas Related to Circles — Flashcards
Karnataka Board · Class 10 · Mathematics
20 flashcards for Areas Related to Circles (Karnataka Board Class 10 Mathematics) to test yourself on key terms and facts.
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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…
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…
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…
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…
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 =…
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…
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…
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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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
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