Areas Related to Circles: Class 10 Important Questions with Answers

20 MCQs (1 mark each)

1. The area of a circle of radius 7 cm is
   (a) 44 cm² (b) 154 cm² (c) 49 cm² (d) 22 cm²
2. The arc of a sector of radius 7 cm and angle 90° is
   (a) 11 cm (b) 22 cm (c) 44 cm (d) 5.5 cm
3. The area of a quadrant of a circle of radius 14 cm is
   (a) 154 cm² (b) 616 cm² (c) 44 cm² (d) 308 cm²
4. The angle swept by a minute hand in 20 minutes is
   (a) 60° (b) 90° (c) 120° (d) 20°
5. A sector has radius 6 cm and arc 10 cm. Its area is
   (a) 60 cm² (b) 30 cm² (c) 16 cm² (d) 15 cm²
6. If the circumference of a circle equals the perimeter of a square of side 11 cm, the radius is
   (a) 7 cm (b) 14 cm (c) 3.5 cm (d) 11 cm
7. The perimeter of a semicircle of radius 7 cm is
   (a) 22 cm (b) 36 cm (c) 44 cm (d) 29 cm
8. The area of a sector of angle θ is $\frac{1}{8}$ of the circle. θ is
   (a) 30° (b) 45° (c) 60° (d) 90°
9. If the radius of a circle is doubled, its area becomes
   (a) double (b) four times (c) half (d) same
10. The area of the segment of a circle of radius 14 cm with 90° at the centre is
    (a) 56 cm² (b) 154 cm² (c) 98 cm² (d) 42 cm²
11. The hour hand moves through ___ in 2 hours.
    (a) 30° (b) 60° (c) 120° (d) 15°
12. Two circles have areas in ratio 4 : 9. Their circumferences are in ratio
    (a) 4 : 9 (b) 2 : 3 (c) 16 : 81 (d) 3 : 2
13. A wheel of diameter 70 cm makes 10 revolutions. Distance covered
    (a) 22 m (b) 2.2 m (c) 220 m (d) 44 m
14. The area of an equilateral △OAB with OA = 6 cm is
    (a) 9√3 cm² (b) 18 cm² (c) 36√3 cm² (d) 6√3 cm²
15. The ratio of areas of a sector of 60° and a sector of 120° of the same circle is
    (a) 1 : 2 (b) 2 : 1 (c) 1 : 4 (d) 1 : 3
16. A sector of 72° has area 20π. The radius is
    (a) 10 (b) 5 (c) 20 (d) 100
17. Area of a circle is 154 cm². Its circumference is
    (a) 22 cm (b) 44 cm (c) 88 cm (d) 77 cm
18. The major sector of a circle of radius 7 cm with minor angle 90° has area
    (a) 38.5 cm² (b) 115.5 cm² (c) 154 cm² (d) 77 cm²
19. An arc of length 22 cm in a circle of radius 21 cm subtends
    (a) 30° (b) 60° (c) 90° (d) 45°
20. If the perimeter and the area of a circle are numerically equal, the radius is
    (a) 1 (b) 2 (c) 4 (d) π

Answer key

1 (b) · 2 (a) · 3 (a) · 4 (c) · 5 (b) · 6 (a) · 7 (b) · 8 (b) · 9 (b) · 10 (a) · 11 (b) · 12 (b) · 13 (a) · 14 (a) · 15 (a) · 16 (a) · 17 (b) · 18 (b) · 19 (b) · 20 (b)

Hints: Q5 $\frac{1}{2}lr$. Q6 $2\pi r=44$. Q7 $22+14$. Q10 154 − 98. Q13 $10\times 220$ cm. Q16 $\frac{1}{5}\pi r^2=20\pi$. Q20 $2\pi r=\pi r^2$.

Assertion–Reason (10)

(a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

1. A: The area of a sector of 90° in a circle of radius 14 cm is 154 cm². R: Sector area $=\frac{\theta }{360}\pi r^2$.
2. A: The perimeter of a sector of radius 7 cm and angle 90° is 11 cm. R: Arc length $=\frac{\theta }{360}\times 2\pi r$.
3. A: A minute hand sweeps 90° in 15 minutes. R: It turns 6° per minute.
4. A: The minor segment of a circle is always smaller than the minor sector. R: Segment = sector − triangle.
5. A: Doubling the radius doubles the area. R: Area = πr².
6. A: Two wipers of 21 cm sweeping 120° each clean 924 cm². R: Each wiper sweeps one third of a circle.
7. A: The area of a semicircle of radius r is $\frac{1}{2}\pi r^2$. R: A semicircle is a sector of angle 180°.
8. A: An arc of 22 cm in a circle of radius 21 cm subtends 90°. R: The circumference of that circle is 132 cm.
9. A: A horse tied at a corner of a square field with a 7 m rope grazes 38.5 m². R: It can graze a quadrant.
10. A: In a circle, a chord at 60° to the centre forms an equilateral triangle with the radii. R: The two radii are equal and the angle between them is 60°.

Key: 1 (a) · 2 (d) · 3 (a) · 4 (a) · 5 (d) · 6 (a) · 7 (a) · 8 (d) · 9 (a) · 10 (a)

Q2: perimeter = 11 + 14 = 25. Q5: area becomes four times. Q8: $\frac{22}{132}\times 360=60°$.

Very short answer (1 mark each)

1. Find the area of a sector of radius 21 cm and angle 120°. Ans. 462 cm²
2. Find the length of an arc of radius 14 cm and angle 45°. Ans. 11 cm
3. The minute hand is 7 cm. Area swept in 15 minutes? Ans. 38.5 cm²
4. Write the formula for the area of a minor segment. Ans. sector − area of △OAB
5. The circumference is 88 cm. Find the radius. Ans. 14 cm
6. A circle is divided into 12 equal sectors. Angle of each? Ans. 30°
7. Find the perimeter of a quadrant of radius 14 cm. Ans. 22 + 28 = 50 cm
8. Sector area 77 cm², r = 14 cm. Find θ. Ans. 45°

Short answer practice (2 marks each)

1. The length of the minute hand of a clock is 21 cm. Find the area swept in 10 minutes.

2. Find the area of a sector whose arc is 22 cm and radius 14 cm.

Short answer practice (3 marks each)

3. A chord of a circle of radius 14 cm subtends 90° at the centre. Find the areas of the minor and major segments.

4. An umbrella has 10 equally spaced ribs; it is a flat circle of radius 35 cm. Find the area between two consecutive ribs.

5. Find the area of the region between two concentric circles of radii 7 cm and 14 cm, within a sector of 30°.

Long answer (5 marks each)

6. A chord AB of a circle of radius 12 cm subtends 120° at the centre O. Find (i) the length of AB (ii) the area of △OAB (iii) the area of the minor segment (π = 3.14, √3 = 1.73).

7. A sprinkler waters a sector of radius 10 m through 135°. A second sprinkler at the same point waters 6 m through the remaining angle. Find the total area watered (π = 3.14).

8. A round table cover of radius 21 cm has a regular hexagon drawn inside it touching the edge; the six segments outside are embroidered at ₹0.50 per cm². Find the cost (√3 = 1.73).