Areas Related to Circles — Class 10 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Areas Related to Circles" — 9 important questions with detailed answers for CBSE board exam preparation.

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TL;DR: Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Areas Related to Circles" — 9 important questions with detailed answers for CBSE b…

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated Jul 23, 2026

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Key Questions Covered:

A sector of a circle has radius 7 cm and central angle 60°. Find the area of …
Find the perimeter of a sector with radius 10.5 cm and arc length 11 cm.
The radius of a circle is 14 cm. Find the area of a segment if the central an…
A circle has two sectors with central angles 120° and 150°. If the radius is …
Find the area of a segment of a circle with radius 5 cm and chord length 6 cm.
The length of an arc of a circle is 22 cm and the radius is 21 cm. Find the a…
+ 3 more questions in the full chapter

Solutions Summary:

Question	Status
A sector of a circle has radius 7 cm and central angle 60…	✓ Solved
Find the perimeter of a sector with radius 10.5 cm and ar…	✓ Solved
The radius of a circle is 14 cm. Find the area of a segme…	✓ Solved
A circle has two sectors with central angles 120° and 150…	✓ Solved
Find the area of a segment of a circle with radius 5 cm a…	✓ Solved
The length of an arc of a circle is 22 cm and the radius …	✓ Solved

Showing 6 of 9 questions

Q1: A sector of a circle has radius 7 cm and central angle 60°. Find the area of the sector. (Use π = 22/7)

Step 1: Area of a sector = (θ/360°) × πr² Step 2: Here, θ = 60°, r = 7 cm, π = 22/7 Step 3: Area = (60°/360°) × (22/7) × 7² Step 4: Area = (1/6) × (22/7) × 49 Step 5: Area = (1/6) × 22 × 7 Step 6: Area = (1/6) × 154 Step 7: Area = 154/6 = 77/3 cm² Step 8: Area ≈ 25.67 cm² Final Answer: 77/3 cm² or approximately 25.67 cm²

Q2: Find the perimeter of a sector with radius 10.5 cm and arc length 11 cm.

Step 1: Perimeter of a sector = 2r + arc length Step 2: Here, r = 10.5 cm, arc length = 11 cm Step 3: Perimeter = 2(10.5) + 11 Step 4: Perimeter = 21 + 11 Step 5: Perimeter = 32 cm Final Answer: 32 cm

Q3: The radius of a circle is 14 cm. Find the area of a segment if the central angle of the corresponding sector is 90°. (Use π = 22/7)

Step 1: Area of segment = Area of sector − Area of triangle Step 2: Area of sector = (θ/360°) × πr² = (90°/360°) × (22/7) × 14² Step 3: Area of sector = (1/4) × (22/7) × 196 Step 4: Area of sector = (1/4) × 22 × 28 Step 5: Area of sector = (1/4) × 616 = 154 cm² Step 6: Area of triangle = (1/2) × r² × sin(θ) = (1/2) × 14² × sin(90°) Step 7: Area of triangle = (1/2) × 196 × 1 = 98 cm² Step 8: Area of segment = 154 − 98 = 56 cm² Final Answer: 56 cm²

Q4: A circle has two sectors with central angles 120° and 150°. If the radius is 6 cm, find the difference between their areas. (Use π = 22/7)

Step 1: Area of sector 1 = (120°/360°) × πr² Step 2: Area of sector 1 = (1/3) × (22/7) × 6² Step 3: Area of sector 1 = (1/3) × (22/7) × 36 Step 4: Area of sector 1 = (1/3) × 22 × 36/7 Step 5: Area of sector 1 = (22 × 12)/7 = 264/7 cm² Step 6: Area of sector 2 = (150°/360°) × πr² Step 7: Area of sector 2 = (5/12) × (22/7) × 36 Step 8: Area of sector 2 = (5/12) × 22 × 36/7 Step 9: Area of sector 2 = (5 × 22 × 3)/7 = 330/7 cm² Step 10: Difference = 330/7 − 264/7 = 66/7 ≈ 9.43 cm² Final Answer: 66/7...

Q5: Find the area of a segment of a circle with radius 5 cm and chord length 6 cm.

Step 1: First, find the central angle using the chord length Step 2: For a chord, chord = 2r × sin(θ/2) Step 3: 6 = 2(5) × sin(θ/2) Step 4: sin(θ/2) = 6/10 = 0.6 Step 5: θ/2 = 36.87°, so θ ≈ 73.74° ≈ 74° (approximately) Step 6: Using cos formula: cos(θ/2) = √(1 − 0.36) = √0.64 = 0.8 Step 7: Area of sector = (θ/360°) × πr² = (74°/360°) × (22/7) × 25 Step 8: Area of sector ≈ 16.09 cm² Step 9: Area of triangle = (1/2) × r² × sin(θ) = (1/2) × 25 × sin(74°) Step 10: Area of triangle ≈ (1/2) × 25 × 0....

Q6: The length of an arc of a circle is 22 cm and the radius is 21 cm. Find the area of the sector. (Use π = 22/7)

Step 1: Arc length = (θ/360°) × 2πr Step 2: 22 = (θ/360°) × 2 × (22/7) × 21 Step 3: 22 = (θ/360°) × 2 × 22 × 3 Step 4: 22 = (θ/360°) × 132 Step 5: θ/360° = 22/132 = 1/6 Step 6: θ = 60° Step 7: Area of sector = (θ/360°) × πr² = (60°/360°) × (22/7) × 21² Step 8: Area of sector = (1/6) × (22/7) × 441 Step 9: Area of sector = (1/6) × 22 × 63 Step 10: Area of sector = (1/6) × 1386 = 231 cm² Final Answer: 231 cm²

Showing 6 of 9 questions. Visit the full page for complete solutions.