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Areas Related to Circles

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 21 questions

11.1 Areas of Sector and Segment of a Circle

21 q

Solved Examples

Worked · 2
  1. 11.1 Eg.1
    Find the area of the sector of a circle with radius 4 cm and of angle 30∘30^\circ. Also, find the area of the corresponding major sector. (Use π=3.14\pi = 3.14)
  2. 11.1 Eg.2
    Find the area of the segment AYB shown in Fig. 11.6, if the radius of the circle is 21 cm and ∠\angleAOB =120∘= 120^\circ. (Use π=227\pi = \dfrac{22}{7})

Exercise 11.1

Practice · 19
  1. Unless stated otherwise, use π=227\pi = \dfrac{22}{7}.
    Ex 11.1 Q1
    Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60∘60^\circ.
  2. Unless stated otherwise, use π=227\pi = \dfrac{22}{7}.
    Ex 11.1 Q2
    Find the area of a quadrant of a circle whose circumference is 22 cm.
  3. Unless stated otherwise, use π=227\pi = \dfrac{22}{7}.
    Ex 11.1 Q3
    The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
  4. Unless stated otherwise, use π=227\pi = \dfrac{22}{7}.
    Ex 11.1 Q6
    A chord of a circle of radius 15 cm subtends an angle of 60∘60^\circ at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use π=3.14\pi = 3.14 and 3=1.73\sqrt{3} = 1.73)
  5. Unless stated otherwise, use π=227\pi = \dfrac{22}{7}.
    Ex 11.1 Q7
    A chord of a circle of radius 12 cm subtends an angle of 120∘120^\circ at the centre. Find the area of the corresponding segment of the circle. (Use π=3.14\pi = 3.14 and 3=1.73\sqrt{3} = 1.73)
  6. Unless stated otherwise, use π=227\pi = \dfrac{22}{7}.
    Ex 11.1 Q10
    An umbrella has 8 ribs which are equally spaced (see Fig. 11.10). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.
  7. Unless stated otherwise, use π=227\pi = \dfrac{22}{7}.
    Ex 11.1 Q11
    A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115∘115^\circ. Find the total area cleaned at each sweep of the blades.
  8. Unless stated otherwise, use π=227\pi = \dfrac{22}{7}.
    Ex 11.1 Q12
    To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80∘80^\circ to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (Use π=3.14\pi = 3.14)
  9. Unless stated otherwise, use π=227\pi = \dfrac{22}{7}.
    Ex 11.1 Q13
    A round table cover has six equal designs as shown in Fig. 11.11. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹ 0.35 per cm2^2. (Use 3=1.7\sqrt{3} = 1.7)
  10. Unless stated otherwise, use π=227\pi = \dfrac{22}{7}. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding : (Use π=3.14\pi = 3.14)
    Ex 11.1 Q4 (i)
    minor segment
  11. Ex 11.1 Q4 (ii)
    major sector
  12. Unless stated otherwise, use π=227\pi = \dfrac{22}{7}. In a circle of radius 21 cm, an arc subtends an angle of 60∘60^\circ at the centre. Find:
    Ex 11.1 Q5 (i)
    the length of the arc
  13. Ex 11.1 Q5 (ii)
    area of the sector formed by the arc
  14. Ex 11.1 Q5 (iii)
    area of the segment formed by the corresponding chord
  15. Unless stated otherwise, use π=227\pi = \dfrac{22}{7}. A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see Fig. 11.8). Find (Use π=3.14\pi = 3.14)
    Ex 11.1 Q8 (i)
    the area of that part of the field in which the horse can graze.
  16. Ex 11.1 Q8 (ii)
    the increase in the grazing area if the rope were 10 m long instead of 5 m.
  17. Unless stated otherwise, use π=227\pi = \dfrac{22}{7}. A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in Fig. 11.9. Find :
    Ex 11.1 Q9 (i)
    the total length of the silver wire required.
  18. Ex 11.1 Q9 (ii)
    the area of each sector of the brooch.
  19. Unless stated otherwise, use π=227\pi = \dfrac{22}{7}.
    Ex 11.1 Q14
    Tick the correct answer in the following : Area of a sector of angle pp (in degrees) of a circle with radius R is
    1. A.
      p180×2πR\dfrac{p}{180} \times 2\pi \text{R}
    2. B.
      p180×πR2\dfrac{p}{180} \times \pi \text{R}^2
    3. C.
      p360×2πR\dfrac{p}{360} \times 2\pi \text{R}
    4. D.
      p720×2πR2\dfrac{p}{720} \times 2\pi \text{R}^2