Gujarat Board Solutions Class 10 Maths Chapter 12 Areas Related to Circles Ex 12.2
Gujarat Board Solutions Class 10 Maths Chapter 12 Areas Related to Circles Ex 12.2
Gujarat Board Textbook Solutions Class 10 Maths Chapter 12 Areas Related to Circles Ex 12.2
Question 1.
Find the area of a sector of a circle with radius 6 cm, if angle of the sector is 60°.
Solution:
Here ∠AOB = 60°
and radius r = 6 cm
Question 6.
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 of the circle. (Use π = 3.14 and √3 = 1.73)
Solution:
Here r = 15 cm
θ = 60°
Question 7.
A chord of circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segments of the circle.
Solution:
Here r = 12 cm
and θ = 120°
Question 8.
A horse is tied to a leg at one corner of a square-shaped grass field of side 15 m by means of a 5 m long rope (see figure). Find:
(i) The area of that part of the field in which the horse can graze.
(ii) The increase in the grazing area of the rope were 10 m long instead of 5 m. (Use π = 3.14)
Question 9.
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 figure find:
Question 10.
An umbrella has 8 ribs which are equally spaced (see figure). Assuming umbrella to be a flat circle of radius 45 cm. Find the area between the two consecutive ribs of the umbrella.
Question 11.
A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through angle of 115°. Find the total area cleaned at each sweep of the blades.
Solution:
Here
r = 25 cm
θ = 115°
Total area cleaned at each sweep of the blades
Question 12.
Two 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 over which the ships are warned. (Use π = 3.14)
Solution:
Here r = 16.5 km
and θ = 80°
The area of the sea over which the ships are warned
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 design at the rate of ₹ 0.35 per cm2. (Use √3 = 1.7)
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
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