Areas Related to Circles Ex 12.2 Solutions
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°. Findthe total area cleaned at each sweep of the blades
Answer - 11 : -
Given,
Radius (r) = 25 cm
Sector angle (θ) = 115°
Since there are 2 blades,
The total area of the sector made by wiper =2×(θ/360°)×π r2
= 2×(115/360)×(22/7)×252
= 2×158125/252 cm2
= 158125/126 = 1254.96 cm2
Question - 12 : - To warn ships forunderwater rocks, a lighthouse spreads a red colored light over a sector ofangle 80° to a distance of 16.5 km.
Answer - 12 : -
Find the area of the sea over which the ships are warned.
(Use π = 3.14)
Solution:
Let O bet the position of Lighthouse.
Here the radius will be the distance overwhich light spreads.
Given, radius (r) = 16.5 km
Sector angle (θ) = 80°
Now, the total area of the sea over which theships are warned = Area made by the sector
Or, Area of sector = (θ/360°)×πr2
= (80°/360°)×πr2 km2
= 189.97 km2
Question - 13 : - A round table cover has six equal designs asshown in Fig. 12.14. If the radius of the cover is 28 cm, find the cost ofmaking the designs at the rate of ₹ 0.35 per cm2 . (Use √3 =1.7)
Answer - 13 : - 
Question - 14 : - Tick the correctsolution in the following:
Answer - 14 : -
Area of a sector of angle p (in degrees) of a circle with radius R is
(A) p/180 × 2πR (B) p/180 × π R_2
(C) p/360 × 2πR (D) p/720 × 2πR_2
Solution:
The area of a sector = (θ/360°)×πr2
Given, θ = p
So, area of sector = p/360×πR2
Multiplying and dividing by 2 simultaneously,
= (p/360)×2/2×πR2
= (2p/720)×2πR2
_So, option (D) is correct