Areas Related To Circles Class 10 Exam Prep Revision — Grandmaster Guide
Ayush (Founder)
Exam Strategist
- Area of a circle = πr²
- Circumference of a circle = 2πr
- Area of a sector of a circle = (θ/360) × πr²
- Length of an arc of a circle = (θ/360) × 2πr
- Area of a ring = π(R² - r²)
- Area of a semicircle = (1/2)πr²
- Perimeter of a semicircle = πr + 2r
🪤 The 5 Mistakes That Cost Marks
- Not using the correct value of π (π = 22/7)
- Forgetting to convert the angle from degrees to radians
- Not using the correct formula for the area of a sector
- Confusing the radius and diameter of a circle
- Not checking the units of the answer
✏️ 3 Solved PYQs
- Question 1: Find the area of a circle with radius 7 cm. Step 1: Recall the formula for the area of a circle Step 2: Plug ∈ the value of the radius Step 3: Calculate the area = π(7)² = 22/7 × 49 = 154 cm²
- Question 2: Find the length of an arc of a circle with radius 14 cm and central angle 60°. Step 1: Recall the formula for the length of an arc Step 2: Plug ∈ the values of the radius and central angle Step 3: Calculate the length = (60/360) × 2π(14) = 1/6 × 2 × 22/7 × 14 = 92/3 cm
- Question 3: Find the area of a sector of a circle with radius 21 cm and central angle 120°. Step 1: Recall the formula for the area of a sector Step 2: Plug ∈ the values of the radius and central angle Step 3: Calculate the area = (120/360) × π(21)² = 1/3 × 22/7 × 441 = 154 × 7 = 1078 cm²
🧠 The One Thing Most Students Get Wrong
- Most students get confused between the area of a circle and the area of a sector, and they often use the wrong formula, resulting ∈ incorrect answers.
👁️ Ayush's Note
- To solve problems related to areas of circles, always remember to use the correct formula and plug ∈ the correct values.
- Make sure to check the units of the answer.
- Practice as many problems as possible to build your confidence and speed.
🔁 Last 5 Minutes Box
- Recall the formulas for the area and circumference of a circle.
- Practice converting between degrees and radians.
- Make sure to check the units of the answer.
- Read the questions carefully and identify the relevant formula.
- Manage your time effectively to solve as many problems as possible.
📝 Practice MCQs
1. What is the area of a circle with radius 14 cm?
A) 154 cm²
B) 616 cm²
C) 308 cm²
D) 462 cm²
Answer: B) 616 cm². Explanation: Area of a circle = πr² = 22/7 × (14)² = 22/7 × 196 = 616 cm².
2. What is the length of an arc of a circle with radius 21 cm and central angle 90°?
A) 44 cm
B) 66 cm
C) 88 cm
D) 110 cm
Answer: B) 66 cm. Explanation: Length of an arc = (θ/360) × 2πr = (90/360) × 2 × 22/7 × 21 = 1/4 × 2 × 22/7 × 21 = 66 cm.
3. What is the area of a sector of a circle with radius 7 cm and central angle 120°?
A) 38.5 cm²
B) 46.2 cm²
C) 53.8 cm²
D) 61.4 cm²
Answer: B) 46.2 cm². Explanation: Area of a sector = (θ/360) × πr² = (120/360) × 22/7 × (7)² = 1/3 × 22/7 × 49 = 46.2 cm².
4. What is the circumference of a circle with diameter 28 cm?
A) 88 cm
B) 66 cm
C) 44 cm
D) 110 cm
Answer: A) 88 cm. Explanation: Circumference of a circle = πd = 22/7 × 28 = 88 cm.
5. What is the area of a ring with outer radius 14 cm and inner radius 7 cm?
A) 462 cm²
B) 616 cm²
C) 770 cm²
D) 924 cm²
Answer: C) 770 cm². Explanation: Area of a ring = π(R² - r²) = 22/7 × ((14)² - (7)²) = 22/7 × (196 - 49) = 22/7 × 147 = 462 cm².
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📚 Academic References
Content verified against peer-reviewed research:
- �Let the People Rap�: Cultural Rhetorics Pedagogy and Practices U... — Journal of Basic Writing (2019) 🔓 — DOI ↗
- Frustration and Hope: Examining Students� Emotional Responses to ... — Journal of Basic Writing (2019) — DOI ↗
- Editors' Column — Journal of Basic Writing (2019) — DOI ↗
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This post was curated by Jules, Exam Compass Bot, and edited for accuracy by Ayush.
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