Areas Related to Circles Quiz - CBSE Class 10 Mathematics

Free practice quiz: Areas Related to Circles (CBSE Class 10 Mathematics). 15 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 10 Mathematics practice quiz has 15 multiple-choice questions on Areas Related to Circles, and 15 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. Find the area of a sector of a circle with radius 14 cm and central angle 90°. Use π = 22/7.

   1. 154 cm²
   2. 308 cm²
   3. 77 cm²
   4. 616 cm²
   Show answer

   Answer: A. 154 cm²

   Area = (90/360) × π × 14² = ¼ × (22/7) × 196 = 154 cm².

2. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the minor segment. Use π = 3.14.

   1. 78.5 cm²
   2. 50 cm²
   3. 21.5 cm²
   4. 28.5 cm²
   Show answer

   Answer: D. 28.5 cm²

   Sector area = ¼ × 3.14 × 10² = 78.5 cm². Triangle area = ½ × 10 × 10 = 50 cm². Segment = 78.5 − 50 = 28.5 cm².

3. Find the length of an arc of a circle of radius 12 cm that subtends a central angle of 45°. Use π = 3.14.

   1. 18.84 cm
   2. 4.71 cm
   3. 37.68 cm
   4. 9.42 cm
   Show answer

   Answer: D. 9.42 cm

   Arc length = (45/360) × 2 × 3.14 × 12 = 1/8 × 75.36 = 9.42 cm.

4. The minute hand of a clock is 14 cm long. How far does its tip move in 15 minutes? Use π = 22/7.

   1. 44 cm
   2. 11 cm
   3. 22 cm
   4. 88 cm
   Show answer

   Answer: C. 22 cm

   In 15 minutes the hand sweeps 90°. Arc length = (90/360) × 2 × (22/7) × 14 = ¼ × 88 = 22 cm.

5. A sector of a circle has perimeter 30 cm and radius 9 cm. Find the central angle of the sector (nearest whole degree). Use π = 3.14.

   1. 60°
   2. 38°
   3. 76°
   4. 120°
   Show answer

   Answer: C. 76°

   Arc length = 30 − 2 × 9 = 12 cm. Using arc length = (θ/360) × 2πr: 12 = (θ/360) × 2 × 3.14 × 9. Thus θ = 12 × 360 ÷ 56.52 ≈ 76.4°, nearest 76°.

More questions in this quiz

Answers and explanations are in the full quiz.

1. An arc of a circle of radius 21 cm subtends a central angle of 60°. Using π = 22/7, find the arc length.
2. What is the perimeter of a sector of radius 10 cm and central angle 36°? Use π = 3.14.
3. A sprinkler sprays water over a sector of angle 120° and radius 7 m. Find the area watered. Use π = 22/7.
4. The area of a sector of a circle is 77 cm² and its radius is 7 cm. Find the central angle of the sector. Use π = 22/7.
5. Find the perimeter of a sector of radius 6 cm and central angle 90°. Use π = 3.14.
6. A chord of a circle of radius 7 cm subtends a central angle of 120°. Find the area of the minor segment. Use π = 22/7 and √3 = 1.732.
7. A sector of a circle with radius 5 cm has central angle 72°. Find its area. Use π = 3.14.
8. An arc of length 11 cm is cut from a circle of radius 7 cm. Find the central angle of the arc. Use π = 22/7.
9. A chord of a circle of radius 6 cm subtends a central angle of 60°. Find the area of the minor segment. Use π = 3.14 and √3 = 1.73.
10. A windshield wiper blade is 21 cm long and sweeps through an angle of 120°. Find the area wiped by the blade. Use π = 22/7.

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