Question 8. 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.). Find
(i) the area of that part of the field in which the horse can graze.
(ii) the increase in the grazing area if the rope were 10 m long instead of 5 m. (Use π = 3.14)
(i) Horse with graze=∅/(360°) × π × r2
= 90°/360° × 3.14 × 5 × 5
Area of circle the length of rope is increased to 10m
=∅/(360°) × π × r2
=90°/360° × 3.14 × 10 × 10
(ii) Increasing in grazing area=78.5m2-19.635m2=58.875m2
Question 9. A brooch is made with silver wire in the form of a circle with a diameter of 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in Fig. Find:
(i) the total length of the silver wire required.
(ii) the area of each sector of the brooch.
(i) Total length of silver wire required=circumference of broach+5diameter
=5 × 35 mm × πd
=175+22/7 × 35
(ii) Area of each sector=1/10×Area of circle
Question 10. An umbrella has 8 ribs that are equally spaced (see Fig.). Assuming the umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.
Total ribs in umbrella=8
Radius of umbrella is =45cm
Area between the two consecutive ribs=1/8π×r2
Question 11. 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 of the blades.
Angle made by sector=∅=115°
Total area clean at each sweep of the blades=2×Area of sector
The total area clean at each sweep of blades=1254.96cm2
Question 12. To warn ships for underwater rocks, a lighthouse spreads a red colored light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned.
(Use π = 3.14)
Distance over which light fall =r=16.5km
Angle made by the sector=∅=80°
Area of the sea over which the ships are warned=Area of sector
The area of ships is +warned =189.97km2
Question 13. A round table cover has six equal designs as shown in Figure. 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)
Total equal designs==6
Cost for making design=RS.035 per cm2
Area of 1 design =Area of sector-Area of triangle
Question 14. Tick the correct answer in the following:
Area of a sector of angle p (in degrees) of a circle with radius R is
(A) p/180 × 2πR (B) p/180 × π R2 (C) p/360 × 2πR (D) p/720 × 2πR2
Area of sector angle p=p/360×2πr2
Therefore, option (D) is correct.