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CBSE · Class 10 · Mathematics

Areas Related to Circles

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
The area of a sector of angle 135° in a circle of radius 7 cm (π = 22/7) is:
  1. 16 1/2 cm2
  2. 115 1/2 cm2
  3. 154 cm2
  4. 57 3/4 cm2
2.
The length of an arc of angle 270° in a circle of radius 35 cm (π = 22/7) is:
  1. 165 cm
  2. 330 cm
  3. 2,887 1/2 cm
  4. 82 1/2 cm
3.
The circumference of a circle is 352 cm (π = 22/7). Its radius is:
  1. 112 cm
  2. 63 cm
  3. 176 cm
  4. 56 cm
4.
The minute hand of a clock is 7 cm long. The area it sweeps in 25 minutes (π = 22/7) is:
  1. 18 1/3 cm2
  2. 10 25/36 cm2
  3. 128 1/3 cm2
  4. 64 1/6 cm2
5.
The area of a sector of angle θ in a circle of radius r is:
  1. (θ/360) × πr2
  2. (θ/360) × 2πr
  3. (θ/180) × πr2
  4. θ × πr2
6.
A sector of a circle of radius 14 cm has an area of 256 2/3 cm2 (π = 22/7). Its angle is:
  1. 150°
  2. 160°
  3. 300°
  4. 210°
7.
A chord of a circular field of radius 91 m makes a right angle at the centre. The area of the minor segment (π = 22/7) is:
  1. 23,660 m2
  2. 6,506 1/2 m2
  3. 4,140 1/2 m2
  4. 2,366 m2
8.
Assertion (A): An arc of angle 270° in a circle of radius 7 cm is 33 cm long (π = 22/7).
Reason (R): The length of an arc of angle θ is (θ/360) × πr2.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
Find the perimeter of a sector of angle 180° in a circle of radius 21 cm (π = 22/7).
10.
Find the area of the ring between two concentric circles of radii 21 cm and 14 cm (π = 22/7).
11.
A wheel has a diameter of 28 cm. How far does it travel in 650 complete turns (π = 22/7)? Give the answer in metres.
12.
Find the area of the major sector of a circle of radius 21 cm when the minor sector has an angle of 90° (π = 22/7).
13.
Find the area of a quadrant of a circle whose circumference is 308 cm (π = 22/7).
14.
The circumference of a circle is 88 cm. Find its area (π = 22/7).
15.
A chord of a circular field of radius 49 m makes a right angle at the centre. Find the area of the major segment (π = 22/7).
16.
An umbrella has 6 equally spaced ribs. Taking it as a flat circle of radius 35 cm, find the area between two neighbouring ribs (π = 22/7).
Section C — Word problems4 × 4 = 16 marks
17.
A horse is tied to a peg at one corner of a square field of side 35 m with a rope 21 m long. (a) What area can it graze? (b) How much more could it graze if the rope were 28 m long? (π = 22/7)
18.
A car has two wipers that do not overlap. Each blade is 42 cm long and sweeps through an angle of 105°. Find the total area cleaned at each sweep (π = 22/7).
19.
A lighthouse spreads a red warning light over a sector of 100° up to a distance of 28 km. Over what area of sea are ships warned (π = 22/7)?
20.
A circular park of radius 35 m has a path 7 m wide around it on the outside. Find the area of the path and the cost of paving it at Rs 41 per m2 (π = 22/7).
AmbifulWorksheets
Practice that never repeats
CBSE · Class 10 · Mathematics

Answer key

Areas Related to Circles · AW-10M-ARC-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) 57 3/4 cm2(135/360) × 22/7 × 72 = 57 3/4
2(a) 165 cm(270/360) × 2 × 22/7 × 35 = 165
3(d) 56 cm2 × 22/7 × r = 352, so r = 56
4(d) 64 1/6 cm225 minutes = 150°; (150/360) × 22/7 × 72
5(a) (θ/360) × πr2—
6(a) 150°θ/360 × 22/7 × 142 = 256 2/3, so θ = 150
7(d) 2,366 m2quadrant − triangle = 6,506 1/2 − 4,140 1/2 = 2366
8(c) A is true, but R is false.A is true: (270/360) × 2 × 22/7 × 7 = 33. R is false.
9108 cm2r + arc = 42 + 66
10770 cm222/7 × (212 − 142) = 770
11572 mone turn = 22/7 × 28 = 88 cm; 650 turns = 57,200 cm
121,039 1/2 cm2major sector angle = 360° − 90° = 270°
131,886 1/2 cm2r = 49; quadrant = (1/4) × 22/7 × 492
14616 cm2r = 14; area = 22/7 × 142
156,860 m2circle − minor segment = 7,546 − 686
16641 2/3 cm222/7 × 352 ÷ 6
17(a) 346 1/2 m2; (b) 269 1/2 m2 morea quadrant each time: (1/4) × 22/7 × r2
183,234 cm22 × (105/360) × 22/7 × 422
19684 4/9 km2(100/360) × 22/7 × 282
201,694 m2; Rs 69,45422/7 × (422 − 352) = 1,694