Class 10 Mathematics
Chapter 11: Areas Related to Circles
50 Practice Questions — All Types Covered
Topics: Area & Perimeter of Circle | Sector | Segment | Combinations | Real-Life Applications
Use π = 22/7 unless stated otherwise
SECTION A — Multiple Choice Questions (1 Mark Each)
1. The area of a circle with radius r is:
(a) 2πr (b) πr2 (c) 2πr2 (d) πd
2. The area of a sector with radius 7 cm and angle 90° is:
(a) 38.5 cm2 (b) 77 cm2 (c) 154 cm2 (d) 19.25 cm2
3. The length of an arc of a sector with radius r and angle θ° is:
(a) (θ/360) × 2πr (b) (θ/180) × πr (c) (θ/360) × πr2 (d) (θ/360) × πr
4. Area of a minor segment = Area of sector −
(a) Area of major sector (b) Area of triangle (c) Area of circle (d) Circumference
5. If the circumference of a circle is 44 cm, its area is:
(a) 77 cm2 (b) 154 cm2 (c) 308 cm2 (d) 616 cm2
6. The perimeter of a semicircle of radius 7 cm is:
(a) 22 cm (b) 36 cm (c) 44 cm (d) 11 cm
7. The area of the major sector of a circle with radius 6 cm and minor sector angle 60° is:
(a) 132π/6 (b) 5πr2/6 (c) 30π cm2 (d) 36π cm2
8. A chord of a circle of radius 10 cm subtends an angle of 60° at the centre. The area of the
corresponding minor segment is (use π = 3.14):
(a) 9.08 cm2 (b) 19.5 cm2 (c) 52.33 cm2 (d) 28.7 cm2
9. The diameter of a wheel is 1.26 m. How many revolutions will it make to cover a distance of 792
m?
(a) 100 (b) 150 (c) 200 (d) 250
10. The area of a quadrant of a circle with radius 14 cm is:
(a) 154 cm2 (b) 77 cm2 (c) 308 cm2 (d) 616 cm2
SECTION B — Very Short Answer Questions (2 Marks Each)
11. Find the area of a sector of a circle with radius 6 cm and angle 60°. (Use π = 3.14)
, 12. The radii of two circles are 19 cm and 9 cm. Find the radius of a circle whose circumference
equals the sum of the circumferences of the two circles.
13. Find the circumference of a circle whose area is 6.16 cm2.
14. A horse is tied to a peg at one corner of a square field of side 15 m by a rope 5 m long. Find the
area of the field in which the horse can graze.
15. Find the area of a sector of a circle with radius 21 cm and arc length 55 cm.
16. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5
minutes.
17. Find the area of a ring whose outer radius is 20 cm and inner radius is 15 cm.
18. A chord of a circle of radius 14 cm makes a right angle at the centre. Find the areas of the minor
and major segments.
19. Find the number of revolutions made by a circular wheel of area 1.54 m2 in rolling a distance of
176 m.
20. The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm. Find the area of the sector.
SECTION C — Short Answer Questions (3 Marks Each)
21. Find the area of the shaded region in the figure where ABCD is a square of side 14 cm and four
circles are drawn with each side of the square as diameter.
22. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find: (i) the length of the
arc, (ii) area of the sector, (iii) area of the segment formed by the corresponding chord.
23. A round table cover has six equal designs as shown. If the radius of the cover is 28 cm, find the
cost of making the designs at the rate of ■0.35 per cm2. (Use √3 = 1.7)
24. Find the area of the shaded region where a circular arc of radius 6 cm has been drawn with vertex
O of an equilateral triangle OAB of side 12 cm as centre.
25. The area of an equilateral triangle ABC is 17320.5 cm2. With each vertex as centre and radius
equal to half the side of the triangle, circles are drawn. Find the area of the region not covered by
circles. (Use π = 3.14, √3 = 1.73205)
26. On a square handkerchief, nine circular designs each of radius 7 cm are made. Find the area of
the remaining portion of the handkerchief.
27. In a circular table of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the
middle as shown. Find the area of the design.
28. A park has a flower bed in the shape of a sector with radius 21 m and angle 120°. A path of width
7 m runs all around the outside edge of the flower bed (also in sector shape). Find the area of the
path.
29. AB and CD are two diameters of a circle with centre O perpendicular to each other and OD is the
diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.
Chapter 11: Areas Related to Circles
50 Practice Questions — All Types Covered
Topics: Area & Perimeter of Circle | Sector | Segment | Combinations | Real-Life Applications
Use π = 22/7 unless stated otherwise
SECTION A — Multiple Choice Questions (1 Mark Each)
1. The area of a circle with radius r is:
(a) 2πr (b) πr2 (c) 2πr2 (d) πd
2. The area of a sector with radius 7 cm and angle 90° is:
(a) 38.5 cm2 (b) 77 cm2 (c) 154 cm2 (d) 19.25 cm2
3. The length of an arc of a sector with radius r and angle θ° is:
(a) (θ/360) × 2πr (b) (θ/180) × πr (c) (θ/360) × πr2 (d) (θ/360) × πr
4. Area of a minor segment = Area of sector −
(a) Area of major sector (b) Area of triangle (c) Area of circle (d) Circumference
5. If the circumference of a circle is 44 cm, its area is:
(a) 77 cm2 (b) 154 cm2 (c) 308 cm2 (d) 616 cm2
6. The perimeter of a semicircle of radius 7 cm is:
(a) 22 cm (b) 36 cm (c) 44 cm (d) 11 cm
7. The area of the major sector of a circle with radius 6 cm and minor sector angle 60° is:
(a) 132π/6 (b) 5πr2/6 (c) 30π cm2 (d) 36π cm2
8. A chord of a circle of radius 10 cm subtends an angle of 60° at the centre. The area of the
corresponding minor segment is (use π = 3.14):
(a) 9.08 cm2 (b) 19.5 cm2 (c) 52.33 cm2 (d) 28.7 cm2
9. The diameter of a wheel is 1.26 m. How many revolutions will it make to cover a distance of 792
m?
(a) 100 (b) 150 (c) 200 (d) 250
10. The area of a quadrant of a circle with radius 14 cm is:
(a) 154 cm2 (b) 77 cm2 (c) 308 cm2 (d) 616 cm2
SECTION B — Very Short Answer Questions (2 Marks Each)
11. Find the area of a sector of a circle with radius 6 cm and angle 60°. (Use π = 3.14)
, 12. The radii of two circles are 19 cm and 9 cm. Find the radius of a circle whose circumference
equals the sum of the circumferences of the two circles.
13. Find the circumference of a circle whose area is 6.16 cm2.
14. A horse is tied to a peg at one corner of a square field of side 15 m by a rope 5 m long. Find the
area of the field in which the horse can graze.
15. Find the area of a sector of a circle with radius 21 cm and arc length 55 cm.
16. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5
minutes.
17. Find the area of a ring whose outer radius is 20 cm and inner radius is 15 cm.
18. A chord of a circle of radius 14 cm makes a right angle at the centre. Find the areas of the minor
and major segments.
19. Find the number of revolutions made by a circular wheel of area 1.54 m2 in rolling a distance of
176 m.
20. The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm. Find the area of the sector.
SECTION C — Short Answer Questions (3 Marks Each)
21. Find the area of the shaded region in the figure where ABCD is a square of side 14 cm and four
circles are drawn with each side of the square as diameter.
22. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find: (i) the length of the
arc, (ii) area of the sector, (iii) area of the segment formed by the corresponding chord.
23. A round table cover has six equal designs as shown. If the radius of the cover is 28 cm, find the
cost of making the designs at the rate of ■0.35 per cm2. (Use √3 = 1.7)
24. Find the area of the shaded region where a circular arc of radius 6 cm has been drawn with vertex
O of an equilateral triangle OAB of side 12 cm as centre.
25. The area of an equilateral triangle ABC is 17320.5 cm2. With each vertex as centre and radius
equal to half the side of the triangle, circles are drawn. Find the area of the region not covered by
circles. (Use π = 3.14, √3 = 1.73205)
26. On a square handkerchief, nine circular designs each of radius 7 cm are made. Find the area of
the remaining portion of the handkerchief.
27. In a circular table of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the
middle as shown. Find the area of the design.
28. A park has a flower bed in the shape of a sector with radius 21 m and angle 120°. A path of width
7 m runs all around the outside edge of the flower bed (also in sector shape). Find the area of the
path.
29. AB and CD are two diameters of a circle with centre O perpendicular to each other and OD is the
diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.
