Class 10 Maths Chapter – 11 Areas Related to Circles Exercise 11.1 Questions and Answers
Exercise 11.1
Q1. Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.
Answer:
Q2. Find the area of a quadrant of a circle whose circumference is 22 cm.
Answer:
Q3. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
Answer: In 5 minutes the hand sweeps 30°.
Q4. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding (i) minor segment (ii) major sector. (Use π = 3.14)
Answer: (i) Minor segment = sector − triangle
(ii) Major sector
Q5. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find
(i) the length of the arc
Answer: (i) Arc length
(ii) area of the sector
Answer: (ii) Sector area
(iii) area of the segment formed by the corresponding chord.
Answer: (iii) Triangle:
Q6. A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments. (Use π = 3.14, √3 = 1.73)
Answer: Sector
Triangle:
Minor segment :
Major segment :
minor segment :
Q7. A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment. (Use π = 3.14, √3 = 1.73)
Answer: Sector:
Triangle:
Segment :
Q8. 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. Find
(i) the area in which the horse can graze
Answer: (i) The horse grazes a quadrant (90°) of radius 5 m:
(ii) the increase in grazing area if the rope were 10 m long. (Use π = 3.14)
Answer: (ii) With rope 10 m:
Q9. 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. Find
(i) total length of silver wire required
Answer:
(ii) area of each sector.
Answer:
Q10. An umbrella has 8 ribs which are equally spaced. Assuming umbrella to be a flat circle of radius 45 cm, find the area between two consecutive ribs.
Answer: Each sector = 45°:
Exactly:
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°. Find the total area cleaned at each sweep.
Answer: One wiper:
Total (two wipers)
Q12. To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea warned. (Use π = 3.14)
Answer:
Q13. A round table cover has six equal designs. 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)
Answer: Each design is a segment of angle 60°. Sector
Triangle (equilateral, side 28 cm):
cm²
One segment :
Six designs:
Cost :
Q14. Tick the correct answer: Area of a sector of angle p (in degrees) of a circle with radius R is (A)
Answer:
since area of sector of angle:
